chapter 4 resource masters 4... · 000i_alg1_a_crm_c04_tp_660499.indd...

Chapter 4 Resource Masters

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All rights reserved. The contents, or parts thereof, may be reproduced in print form for non-profit educational use with Glencoe Algebra 1, provided such reproductions bear copyright notice, but may not be reproduced in any form for any other purpose without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, network storage or transmission, or broadcast for distance learning.

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ISBN: 978-0-07-660499-9MHID: 0-07-660499-3

Printed in the United States of America.

1 2 3 4 5 6 7 8 9 DOH 16 15 14 13 12 11

CONSUMABLE WORKBOOKS Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish.

MHID ISBNStudy Guide and Intervention Workbook 0-07-660292-3 978-0-07-660292-6Homework Practice Workbook 0-07-660291-5 978-0-07-660291-9

Spanish VersionHomework Practice Workbook 0-07-660294-X 978-0-07-660294-0

Answers For Workbooks The answers for Chapter 4 of these workbooks can be found in the back of this Chapter Resource Masters booklet.

ConnectED All of the materials found in this booklet are included for viewing, printing, and editing at connected.mcgraw-hill.com.

Spanish Assessment Masters (MHID: 0-07-660289-3, ISBN: 978-0-07-660289-6) These masters contain a Spanish version of Chapter 4 Test Form 2A and Form 2C.

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iii

Teacher’s Guide to Using the Chapter 4 Resource Masters ..............................................iv

Chapter Resources Chapter 4 Student-Built Glossary ...................... 1Chapter 4 Anticipation Guide (English) ............. 3Chapter 4 Anticipation Guide (Spanish) ............ 4

Lesson 4-1Graphing Equations in Slope-Intercept Form Study Guide and Intervention ............................ 5Skills Practice .................................................... 7Practice ............................................................. 8Word Problem Practice ...................................... 9Enrichment ...................................................... 10

Lesson 4-2Writing Equations in Slope-Intercept Form Study Guide and Intervention ...........................11Skills Practice .................................................. 13Practice ........................................................... 14Word Problem Practice .................................... 15Enrichment ...................................................... 16

Lesson 4-3Writing Equations in Point-Slope FormStudy Guide and Intervention .......................... 17Skills Practice .................................................. 19Practice ........................................................... 20Word Problem Practice .................................... 21Enrichment ...................................................... 22Graphing Calculator Activity ............................ 23

Lesson 4-4Parallel and Perpendicular Lines Study Guide and Intervention .......................... 24Skills Practice .................................................. 26Practice ........................................................... 27Word Problem Practice .................................... 28Enrichment ...................................................... 29

Lesson 4-5Scatter Plots and Lines of Fit Study Guide and Intervention .......................... 30Skills Practice .................................................. 32Practice ........................................................... 33Word Problem Practice .................................... 34Enrichment ...................................................... 35Spreadsheet Activity ........................................ 36

Lesson 4-6Regression and Median-Fit Lines Study Guide and Intervention .......................... 37Skills Practice .................................................. 39Practice ........................................................... 40Word Problem Practice .................................... 41Enrichment ...................................................... 42

Lesson 4-7Inverse Linear FunctionsStudy Guide and Intervention .......................... 43Skills Practice .................................................. 45Practice ........................................................... 46Word Problem Practice .................................... 47Enrichment ...................................................... 48

AssessmentStudent Recording Sheet ................................ 49Rubric for Scoring Extended Response .......... 50Chapter 4 Quizzes 1 and 2 ............................. 51Chapter 4 Quizzes 3 and 4 ............................. 52Chapter 4 Mid-Chapter Test ............................ 53Chapter 4 Vocabulary Test ............................... 54Chapter 4 Test, Form 1 .................................... 55Chapter 4 Test, Form 2A ................................. 57

Chapter 4 Test, Form 2B ................................. 59Chapter 4 Test Form 2C .................................. 61Chapter 4 Test Form 2D .................................. 63Chapter 4 Test Form 3 ..................................... 65Chapter 4 Extended-Response Test ................ 67Standardized Test Practice .............................. 68

Answers ........................................... A1–A34

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Teacher’s Guide to Using the Chapter 4 Resource Masters

The Chapter 4 Resource Masters includes the core materials needed for Chapter 4. These materials include worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet.

All of the materials found in this booklet are included for viewing, printing, and editing at connectED.mcgraw-hill.com.

Chapter Resources

Student-Built Glossary (pages 1–2) These masters are a student study tool that presents up to twenty of the key vocabulary terms from the chapter. Students are to record definitions and/or examples for each term. You may suggest that students highlight or star the terms with which they are not familiar. Give this to students before beginning Lesson 4-1. Encourage them to add these pages to their mathematics study notebooks. Remind them to complete the appropriate words as they study each lesson.

Anticipation Guide (pages 3–4) This master, presented in both English and Spanish, is a survey used before beginning the chapter to pinpoint what students may or may not know about the concepts in the chapter. Students will revisit this survey after they complete the chapter to see if their perceptions have changed.

Lesson ResourcesStudy Guide and Intervention These masters provide vocabulary, key concepts, additional worked-out examples and Check Your Progress exercises to use as a reteaching activity. It can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent.

Skills Practice This master focuses more on the computational nature of the lesson. Use as an additional practice option or as homework for second-day teaching of the lesson.

Practice This master closely follows the types of problems found in the Exercises section of the Student Edition and includes word problems. Use as an additional practice option or as homework for second-day teaching of the lesson.

Word Problem Practice This master includes additional practice in solving word problems that apply the concepts of the lesson. Use as an additional practice or as homework for second-day teaching of the lesson.

Enrichment These activities may extend the concepts of the lesson, offer an historical or multicultural look at the concepts, or widen students’ perspectives on the mathematics they are learning. They are written for use with all levels of students.

Graphing Calculator, TI-Nspire, or Spreadsheet Activities These activities present ways in which technology can be used with the concepts in some lessons of this chapter. Use as an alternative approach to some concepts or as an integral part of your lesson presentation.

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Assessment OptionsThe assessment masters in the Chapter 4 Resource Masters offer a wide range of assessment tools for formative (monitoring) assessment and summative (final) assessment.

Student Recording Sheet This master corresponds with the standardized test practice at the end of the chapter.

Extended Response Rubric This master provides information for teachers and stu-dents on how to assess performance on open-ended questions.

Quizzes Four free-response quizzes offer assessment at appropriate intervals in the chapter.

Mid-Chapter Test This 1-page test provides an option to assess the first half of the chapter. It parallels the timing of the Mid-Chapter Quiz in the Student Edition and includes both multiple-choice and free-response questions.

Vocabulary Test This test is suitable for all students. It includes a list of vocabulary words and 11 questions to assess students’ knowledge of those words. This can also be used in conjunction with one of the leveled chapter tests.

Leveled Chapter Tests

• Form 1 contains multiple-choice ques-tions and is intended for use with below grade level students.

• Forms 2A and 2B contain multiple-choice questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations.

• Forms 2C and 2D contain free-response questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations.

• Form 3 is a free-response test for use with above grade level students.

All of the above mentioned tests include a free-response Bonus question.

Extended-Response Test Performance assessment tasks are suitable for all students. Sample answers and a scoring rubric are included for evaluation.

Standardized Test Practice These three pages are cumulative in nature. It includes three parts: multiple-choice questions with bubble-in answer format, griddable questions with answer grids, and short-answer free-response questions.

Answers• The answers for the Anticipation Guide

and Lesson Resources are provided as reduced pages.

• Full-size answer keys are provided for the assessment masters.

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Chapter 4 1 Glencoe Algebra 1

Student-Built Glossary

This is an alphabetical list of the key vocabulary terms you will learn in Chapter 4. As you study the chapter, complete each term’s definition or description. Remember to add the page number where you found the term. Add these pages to your Algebra Study Notebook to review vocabulary at the end of the chapter.

Vocabulary TermFound

on PageDefi nition/Description/Example

best-fit line

bivariate data

correlation coefficientkawr·uh·LAY·shun

inverse function

inverse relation

line of fit

linear extrapolationihk·STRA·puh·LAY·shun

linear interpolationihn·TUHR·puh·LAY·shun

(continued on the next page)

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Student-Built Glossary (continued)

Vocabulary TermFound

on PageDefi nition/Description/Example

linear regression

median-fit line

parallel lines

perpendicular linesPUHR·puhn·DIH·kyuh·luhr

residual

scatter plot

slope-intercept formIHN·tuhr·SEHPT


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Anticipation GuideEquations of Linear Functions

Before you begin Chapter 4

• Read each statement.

• Decide whether you Agree (A) or Disagree (D) with the statement.

• Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).

After you complete Chapter 4

• Reread each statement and complete the last column by entering an A or a D.

• Did any of your opinions about the statements change from the first column?

• For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.

STEP 1A, D, or NS

StatementSTEP 2A or D

1. The slope of a line given by an equation in the form y = mx + b can be determined by looking at the equation.

2. The y-intercept of y = 12x - 8 is 8. 3. If two points on a line are known, then an equation can be

written for that line. 4. An equation in the form y = mx + b is in point-slope form. 5. If a pair of lines are parallel, then they have the same slope. 6. Lines that intersect at right angles are called perpendicular

lines. 7. A scatter plot is said to have a negative correlation when the

points are random and show no relationship between x and y.

8. The closer the correlation coefficient is to zero, the more closely a best-fit line models a set of data.

9. The equations of a regression line and a median-fit line are very similar.

10. An inverse relation is obtained by exchanging the x-coordinates with the y-coordinates of each ordered pair of the original relation.

Step 1

Step 2


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Capítulo 4 4 Álgebra 1 de Glencoe

4 Ejercicios preparatoriosEcuaciones de Funciones Lineales

Antes de comenzar el Capítulo 4

• Lee cada enunciado.

• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.

• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta, escribe NS (No estoy seguro(a)).

Después de completar el Capítulo 4

• Vuelve a leer cada enunciado y completa la última columna con una A o una D.

• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?

• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con los enunciados que marcaste con una D.

PASO 1A, D, o NS

EnunciadoPASO 2A o D

1. La pendiente de una recta dada por una ecuación de la forma y = mx + b se puede determinar mediante la observación de la ecuación.

2. La intersección y de y = 12x - 8 es 8. 3. Si se conocen dos puntos sobre una recta, entonces se puede

escribir una ecuación para esa recta. 4. Una ecuación de la forma y = mx + b está en forma

punto-pendiente.

6. A las rectas que se intersecan en ángulos rectos se lesllama rectas perpendiculares.

7. Se dice que un diagrama de dispersión tiene correlación negativa cuando los puntos son aleatorios y no muestran relación entre x y y.

8. Entre más cercano se encuentre de cero el coeficiente de correlación, mejor modela un conjunto de datos la recta de mejor ajuste.

9. La ecuación de una línea de regresión y una recta de mediano ajuste son muy parecidas.

10. Una relación inversa es obtenida cambiando las x-coordenadas con las y-coordenadas de cada par pedido de la relación original.

Paso 1

Paso 2

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Study Guide and InterventionGraphing Equations in Slope-Intercept Form

Slope-Intercept FormSlope-Intercept Form y = mx + b, where m is the slope and b is the y-intercept

Write an equation in slope-intercept form for the line with a slope of -4 and a y-intercept of 3.

y = mx + b Slope-intercept form

y = -4x + 3 Replace m with -4 and b with 3.

Graph 3x - 4y = 8.

3x - 4y = 8 Original equation

-4y = -3x + 8 Subtract 3x from each side.

-4y

−

-4 = -3x + 8 −

-4 Divide each side by -4.

y = 3 −

4 x - 2 Simplify.

The y-intercept of y = 3 −

4 x - 2 is -2 and the slope is 3 −

4 . So graph the point (0, -2). From

this point, move up 3 units and right 4 units. Draw a line passing through both points.

ExercisesWrite an equation of a line in slope-intercept form with the given slope and y-intercept.

1. slope: 8, y-intercept -3 2. slope: -2, y-intercept -1 3. slope: -1, y-intercept -7

Write an equation in slope-intercept form for each graph shown.

4.

(0, –2)

(1, 0) x

y

O

5.

(3, 0)

(0, 3)

x

y

O

6.

(4, –2)

(0, –5)

xy

O

Graph each equation.

7. y = 2x + 1 8. y = -3x + 2 9. y = -x - 1

x

y

O

x

y

O

x

y

O

(0, –2)

(4, 1)

x

y

O

3x - 4y = 8

Example 1

Example 2


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Study Guide and Intervention (continued)

Graphing Equations in Slope-Intercept Form

Modeling Real-World Data

MEDIA Since 1999, the number of music cassettes sold has decreased by an average rate of 27 million per year. There were 124 million music cassettes sold in 1999.

a. Write a linear equation to find the average number of music cassettes sold in any year after 1999.

The rate of change is -27 million per year. In the first year, the number of music cassettes sold was 124 million. Let N = the number of millions of music cassettes sold. Let x = the number of years since 1999. An equation is N = -27x + 124.

b. Graph the equation. The graph of N = -27x + 124 is a line that passes

through the point at (0, 124) and has a slope of -27.

c. Find the approximate number of music cassettes sold in 2003.

N = -27x + 124 Original equation

N = -27(4) + 124 Replace x with 4.

N = 16 Simplify.

There were about 16 million music cassettes sold in 2003.

Exercises 1. MUSIC In 2001, full-length cassettes represented 3.4% of

total music sales. Between 2001 and 2006, the percent decreased by about 0.5% per year.a. Write an equation to find the percent P of recorded music

sold as full-length cassettes for any year x between 2001 and 2006.

b. Graph the equation on the grid at the right.c. Find the percent of recorded music sold

as full-length cassettes in 2004.

2. POPULATION The population of the United States is projected to be 300 million by the year 2010. Between 2010 and 2050, the population is expected to increase by about 2.5 million per year.a. Write an equation to find the population P in any year x

between 2010 and 2050. b. Graph the equation on the grid at the right.

c. Find the population in 2050.

Full-length Cassette Sales

Perc

ent o

f Tot

al M

usic

Sal

es

1.5%

2.0%

1.0%

2.5%

3.0%

3.5%

Years Since 20013210 54

Projected UnitedStates Population

Years Since 2010

Popu

latio

n (m

illio

ns)

0 20 40 x

P

400

380

360

340

320

300

Music Cassettes Sold

Cass

ette

s (m

illio

ns)

50

75

25

0

100

125

Years Since 1999321 5 74 6

Example


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Skills PracticeGraphing Equations in Slope-Intercept Form

Write an equation of a line in slope-intercept form with the given slope and y-intercept.

1. slope: 5, y-intercept: -3 2. slope: -2, y-intercept: 7

3. slope: -6, y-intercept: -2 4. slope: 7, y-intercept: 1

5. slope: 3, y-intercept: 2 6. slope: -4, y-intercept: -9

7. slope: 1, y-intercept: -12 8. slope: 0, y-intercept: 8


9.

(2, 1)

(0, –3)

x

y

O

10.

(0, 2)

(2, –4)

x

y

O

11.

(0, –1)(2, –3)

x

y

O

Graph each equation. 12. y = x + 4 13. y = -2x - 1 14. x + y = -3

x

y

O

x

y

O

x

y

O

15. VIDEO RENTALS A video store charges $10 for a rental card plus $2 per rental.

a. Write an equation in slope-intercept form for the total cost c of buying a rental card and renting m movies.

b. Graph the equation.

c. Find the cost of buying a rental card and renting 6 movies.

Video StoreRental Costs

Tota

l Cos

t ($)

10

0

12

14

16

18

20

c

Movies Rented1 2 3 4 5 m


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PracticeGraphing Equations in Slope-Intercept Form

Write an equation of a line in slope-intercept form with the given slope and y-intercept.

1. slope: 1 −

4 , y-intercept: 3 2. slope: 3 −

2 , y-intercept: -4

3. slope: 1.5, y-intercept: -1 4. slope: -2.5, y-intercept: 3.5


5.

(–5, 0)

(0, 2)

x

y

O

6.

(–2, 0)

(0, 3)

x

y

O

7.

(–3, 0)

(0, –2)

x

y

O

Graph each equation.

8. y = -

1 −

2 x + 2 9. 3y = 2x - 6 10. 6x + 3y = 6

x

y

O

x

y

O

x

y

O

11. WRITING Carla has already written 10 pages of a novel. She plans to write 15 additional pages per month until she is finished.

a. Write an equation to find the total number of pages P written after any number of months m.

b. Graph the equation on the grid at the right.

c. Find the total number of pages written after 5 months.

Carla’s Novel

Months

Page

s W

ritte

n

20 4 61 3 5 m

P

100

80

60

40

20


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Word Problem PracticeGraphing Equations in Slope-Intercept Form

1. SAVINGS Wade’s grandmother gave him $100 for his birthday. Wade wants to save his money to buy a new MP3 player that costs $275. Each month, he adds $25 to his MP3 savings. Write an equation in slope-intercept form for x, the number of months that it will take Wade to save $275.

2. CAR CARE Suppose regular gasoline costs $2.76 per gallon. You can purchase a car wash at the gas station for $3. The graph of the equation for the cost of x gallons of gasoline and a car wash is shown below. Write the equation in slope-intercept form for the line.

Gasoline (gal)3210 54 987 10

y

x6

Co

st o

f g

as a

nd

car

was

h (

$)

6

8

4

2

10

16

14

12

18

24

22

20

(4, 14.04)

(2, 8.52)

(0, 3)

3. ADULT EDUCATION Angie’s mother wants to take some adult education classes at the local high school. She has to pay a one-time enrollment fee of $25 to join the adult education community, and then $45 for each class she wants to take. The equation y = 45x + 25 expresses the cost of taking x classes. What are the slope and y-intercept of the equation?

4. BUSINESS A construction crew needs to rent a trench digger for up to a week. An equipment rental company charges $40 per day plus a $20 non-refundable insurance cost to rent a trench digger. Write and graph an equation to find the total cost to rent the trench digger for d days.

Days3210 54 9876

Pric

e ($

)

100

140

60

20

180

300

340

260

220

5. ENERGY From 2002 to 2005, U.S. consumption of renewable energy increased an average of 0.17 quadrillion BTUs per year. About 6.07 quadrillion BTUs of renewable power were produced in the year 2002.

a. Write an equation in slope-intercept form to find the amount of renewable power P (quadrillion BTUs) produced in year y between 2002 and 2005.

b. Approximately how much renewable power was produced in 2005?

c. If the same trend continues from 2006 to 2010, how much renewable power will be produced in the year 2010?


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Enrichment

Using Equations: Ideal WeightYou can find your ideal weight as follows.A woman should weigh 100 pounds for the first 5 feet of height and 5 additional pounds for each inch over 5 feet (5 feet = 60 inches). A man should weigh 106 pounds for the first 5 feet of height and 6 additional pounds for each inch over 5 feet. These formulas apply to people with normal bone structures.To determine your bone structure, wrap your thumb and index finger around the wrist of your other hand. If the thumb and finger just touch, you have normal bone structure. If they overlap, you are small-boned. If they don’t overlap, you are large-boned. Small-boned people should decrease their calculated ideal weight by 10%. Large-boned people should increase the value by 10%.

Calculate the ideal weights of these people.1. woman, 5 ft 4 in., normal-boned 2. man, 5 ft 11 in., large-boned

3. man, 6 ft 5 in., small-boned 4. you, if you are at least 5 ft tall

For Exercises 5–9, use the following information.

Suppose a normal-boned man is x inches tall. If he is at least 5 feet tall, then x - 60 represents the number of inches this man is over 5 feet tall. For each of these inches, his ideal weight is increased by 6 pounds. Thus, his proper weight y is given by the formula y = 6(x - 60) + 106 or y = 6x - 254. If the man is large-boned, the formula becomes y = 6x - 254 + 0.10(6x - 254).

5. Write the formula for the weight of a large-boned man in slope-intercept form.

6. Derive the formula for the ideal weight y of a normal-boned female with height x inches. Write the formula in slope-intercept form.

7. Derive the formula in slope-intercept form for the ideal weight y of a large-boned female with height x inches.

8. Derive the formula in slope-intercept form for the ideal weight y of a small-boned male with height x inches.

9. Find the heights at which the ideal weights of normal-boned malesand large-boned females would be the same.


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ExercisesWrite an equation of the line that passes through the given point and has the given slope.

1. (3, 5)

x

y

O

m = 2

2.

(0, 0)x

y

O

m = –2

3.

(2, 4)

x

y

O

m = 12

4. (8, 2); slope -

3 −

4 5. (-1, -3); slope 5 6. (4, -5); slope -

1 −

2

7. (-5, 4); slope 0 8. (2, 2); slope 1 −

2 9. (1, -4); slope -6

10. (-3, 0), m = 2 11. (0, 4), m = -3 12. (0, 350), m = 1 −

5

Study Guide and InterventionWriting Equations in Slope-Intercept Form

Write an Equation Given the Slope and a Point

Write an equation ofthe line that passes through (-4, 2) with a slope of 3.The line has slope 3. To find the y-intercept, replace m with 3 and (x, y) with (-4, 2) in the slope-intercept form. Then solve for b. y = mx + b Slope-intercept form

2 = 3(-4) + b m = 3, y = 2, and x = -4

2 = -12 + b Multiply.

14 = b Add 12 to each side.

Therefore, the equation is y = 3x + 14.

Write an equation of the linethat passes through (-2, -1) with a slope of 1 −

4 .

The line has slope 1 −

4 . Replace m with 1 −

4 and (x, y)

with (-2, -1) in the slope-intercept form. y = mx + b Slope-intercept form

-1 = 1 −

4 (-2) + b m = 1

−

4 , y = -1, and x = -2

-1 = - 1 −

2 + b Multiply.

- 1 −

2 = b Add

1

−

2 to each side.

Therefore, the equation is y = 1 −

4 x - 1 −

2 .

Example 1 Example 2


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Writing Equations in Slope-Intercept Form

Write an Equation Given Two Points

Write an equation of the line that passes through (1, 2) and (3, -2). Find the slope m. To find the y-intercept, replace m with its computed value and (x, y) with (1, 2) in the slope-intercept form. Then solve for b.

m = y 2 - y 1 − x 2 - x 1

Slope formula

m = -2 - 2 −

3 - 1 y

2 = -2, y

1 = 2, x

2 = 3, x

1 = 1

m = -2 Simplify.

y = mx + b Slope-intercept form

2 = -2(1) + b Replace m with -2, y with 2, and x with 1.

2 = -2 + b Multiply.

4 = b Add 2 to each side.

Therefore, the equation is y = -2x + 4.

ExercisesWrite an equation of the line that passes through each pair of points.

1. (1, 1)

(0, –3)

x

y

O

2. (0, 4)

(4, 0) x

y

O

3.

(0, 1)

(–3, 0) x

y

O

4. (-1, 6), (7, -10) 5. (0, 2), (1, 7) 6. (6, -25), (-1, 3)

7. (-2, -1), (2, 11) 8. (10, -1), (4, 2) 9. (-14, -2), (7, 7)

10. (4, 0), (0, 2) 11. (-3, 0), (0, 5) 12. (0, 16), (-10, 0)

Example


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Write an equation of the line that passes through the given point with the given slope.

1.

(–1, 4)

x

y

O

m = –3

2. (4, 1)

x

y

O

m = 1

3.

(-1, 2)

x

y

O

m = 2

4. (1, 9); slope 4 5. (4, 2); slope -2 6. (2, -2); slope 3

7. (3, 0); slope 5 8. (-3, -2); slope 2 9. (-5, 4); slope -4

Write an equation of the line that passes through each pair of points.

10. (–2, 3)

(3, –2)

x

y

O

11.

(–1, –3)

(1, 1)x

y

O

12.

(2, –1)

(0, 3)

x

y

O

13. (1, 3), (-3, -5) 14. (1, 4), (6, -1) 15. (1, -1), (3, 5)

16. (-2, 4), (0, 6) 17. (3, 3), (1, -3) 18. (-1, 6), (3, -2)

19. INVESTING The price of a share of stock in XYZ Corporation was $74 two weeks ago. Seven weeks ago, the price was $59 a share.

a. Write a linear equation to find the price p of a share of XYZ Corporation stock w weeks from now.

b. Estimate the price of a share of stock five weeks ago.

Skills PracticeWriting Equations in Slope-Intercept Form

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PracticeWriting Equations in Slope-Intercept Form

Write an equation of the line that passes through the given point and has the given slope.

1.

(1, 2)

x

y

O

m = 3

2.

(–2, 2)

x

y

O

m = –2

3.

(–1, –3)

x

y

O

m = –1

4. (-5, 4); slope -3 5. (4, 3); slope 1 −

2 6. (1, -5); slope -

3 −

2

7. (3, 7); slope 2 −

7 8.

(

-2, 5 −

2 )

; slope -

1 −

2 9. (5, 0); slope 0

Write an equation of the line that passes through each pair of points.

10.

(4, –2)

(2, –4)

x

y

O

11. (0, 5)

(4, 1)x

y

O

12. (–3, 1)

(–1, –3)

x

y

O

13. (0, -4), (5, -4) 14. (-4, -2), (4, 0) 15. (-2, -3), (4, 5)

16. (0, 1), (5, 3) 17. (-3, 0), (1, -6) 18. (1, 0), (5, -1)

19. DANCE LESSONS The cost for 7 dance lessons is $82. The cost for 11 lessons is $122. Write a linear equation to find the total cost C for ℓ lessons. Then use the equation to find the cost of 4 lessons.

20. WEATHER It is 76°F at the 6000-foot level of a mountain, and 49°F at the 12,000-foot level of the mountain. Write a linear equation to find the temperature T at an elevation x on the mountain, where x is in thousands of feet.

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Word Problem PracticeWriting Equations in Slope-Intercept Form

1. FUNDRAISING Yvonne and her friends held a bake sale to benefit a shelter for homeless people. The friends sold 22 cakes on the first day and 15 cakes on the second day of the bake sale. They collected $88 on the first day and $60 on the second day. Let x represent the number of cakes sold and y represent the amount of money made. Find the slope of the line that would pass through the points given.

2. JOBS Mr. Kimball receives a $3000 annual salary increase on the anniversary of his hiring if he receives a satisfactory performance review. His starting salary was $41,250. Write an equation to show k, Mr. Kimball’s salary after t years at this company if his performance reviews are always satisfactory.

3. CENSUS The population of Laredo, Texas, was about 215,500 in 2007. It was about 123,000 in 1990. If we assume that the population growth is constant and t represents the number of years after 1990, write a linear equation to find p, Laredo’s population for any year after 1990.

4. WATER Mr. Williams pays $40 a month for city water, no matter how many gallons of water he uses in a given month. Let x represent the number of gallons of water used per month. Let yrepresent the monthly cost of the city water in dollars. What is the equation of the line that represents this information? What is the slope of the line?

5. SHOE SIZES The table shows how women’s shoe sizes in the United Kingdom compare to women’s shoe sizes in the United States.

Women’s Shoe Sizes

U.K. 3 3.5 4 4.5 5 5.5 6

U.S. 5.5 6 6.5 7 7.5 8 8.5

Source: DanceSport UK

a. Write a linear equation to determine any U.S. size y if you are given the U.K. size x.

b. What are the slope and y-intercept of the line?

c. Is the y-intercept a valid data point for the given information?

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Tangent to a CurveA tangent line is a line that intersects a curve at a point with the same rate of change, or slope, as the rate of change of the curve at that point.

For quadratic functions, functions of the form y = ax2 + bx + c, equations of the tangent lines

can be found. This is based on the fact that the slope through any two points on the curve is equal to the slope of the line tangent to the curve at the point whose x-value is halfway between the x-values of the other two points.

Find an equation of the line tangent to the curve y = x2 + 3x + 2 through the point (2, 12).

First find two points on the curve whose x-values are equidistant from the x-value of (2, 12).

Step 1: Find two points on the curve. Use x = 1 and x = 3. When x = 1, y = 12 + 3(1) + 2 or 6. When x = 3, y = 32 + 3(3) + 2 or 20. So, the two ordered pairs are (1, 6) and (3, 20).

Step 2: Find the slope of the line that passes through these two points. m = 20 - 6 −

3 - 1 or 7

Step 3: Now use this slope and the point (2, 12) to find an equation of the tangent line. y = mx + b Slope-intercept form

12 = 7(2) + b Replace x with 2, y with 12, and m with 7.

-2 = b Solve for b.

So, an equation of the tangent line to y = x2 + 3x + 2 through the point (2, 12) is y = 7x – 2.

ExercisesFind an equation of the line tangent to each curve through the given point.

1. y = x2 - 3x + 7, (2, 5) 2. y = 3x2 + 4x - 5, (-4, 27) 3. y = 5 - x2, (1, 4)

4. Find the slope of the line tangent to the curve at x = 0 for the general equation y = ax2 + bx + c.

5. Find the slope of the line tangent to the curve y = ax2 + bx + c at x by finding the slope of the line through the points (0, c) and (2x, 4ax2 + 2bx + c). Does this equation find the same slope for x = 0 as you found in Exercise 4?

Enrichment

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xO

Example

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Study Guide and InterventionWriting Equations in Point-Slope Form

Point-Slope Form

Point-Slope Formy - y

1 = m(x - x

1), where (x

1, y

1) is a given point on a nonvertical line

and m is the slope of the line

Write an equation in point-slope form for the line that passes through (6, 1) with a slope of -

5 −

2 .

y - y1 = m(x - x1) Point-slope form

y - 1 = -

5 −

2 (x - 6) m = - 5 −

2 ; (x

1, y

1) = (6, 1)

Therefore, the equation is y - 1 = -

5 −

2 (x - 6).

Write an equation in point-slope form for a horizontal line that passes through (4, -1).

y - y1 = m(x - x1) Point-slope form

y - (-1) = 0(x - 4) m = 0; (x1, y

1) = (4, -1)

y + 1 = 0 Simplify.

Therefore, the equation is y + 1 = 0.

ExercisesWrite an equation in point-slope form for the line that passes through each point with the given slope.

1. (4, 1)

x

y

O

m = 1

2.

(–3, 2)

x

y

O

m = 0 3.

(2, –3)

x

y

O

m = –2

4. (2, 1), m = 4 5. (-7, 2), m = 6 6. (8, 3), m = 1

7. (-6, 7), m = 0 8. (4, 9), m = 3 −

4 9. (-4, -5), m = -

1 −

2

10. Write an equation in point-slope form for a horizontal line that passes through (4, -2).

11. Write an equation in point-slope form for a horizontal line that passes through (-5, 6).

12. Write an equation in point-slope form for a horizontal line that passes through (5, 0).

Example 1 Example 2

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Writing Equations in Point-Slope Form

Forms of Linear EquationsSlope-Intercept

Formy = mx + b m = slope; b = y-intercept

Point-Slope Form

y - y1 = m(x - x

1) m = slope; (x

1, y

1) is a given point

Standard

FormAx + By = C

A and B are not both zero. Usually A is nonnegative and A, B, and

C are integers whose greatest common factor is 1.

Write y + 5 = 2 −

3 (x - 6) in

standard form.

y + 5 = 2 −

3 (x - 6) Original equation

3(y + 5) = 3 ( 2 −

3 ) (x - 6) Multiply each side by 3.

3y + 15 = 2(x - 6) Distributive Property

3y + 15 = 2x - 12 Distributive Property

3y = 2x - 27 Subtract 15 from each side.

-2x + 3y = -27 Add -2x to each side.

2x - 3y = 27 Multiply each side by -1.

Therefore, the standard form of the equation is 2x - 3y = 27.

Write y - 2 = - 1 −

4 (x - 8) in

slope-intercept form.

y - 2 = -

1 −

4 (x - 8) Original equation

y - 2 = -

1 −

4 x + 2 Distributive Property

y = -

1 −

4 x + 4 Add 2 to each side.

Therefore, the slope-intercept form of the equation is y = -

1 −

4 x + 4.

ExercisesWrite each equation in standard form.

1. y + 2 = -3(x - 1) 2. y - 1 = -

1 −

3 (x - 6) 3. y + 2 = 2 −

3 (x - 9)

4. y + 3 = -(x - 5) 5. y - 4 = 5 −

3 (x + 3) 6. y + 4 = -

2 −

5 (x - 1)

Write each equation in slope-intercept form.

7. y + 4 = 4(x - 2) 8. y - 5 = 1 −

3 (x - 6) 9. y - 8 = -

1 −

4 (x + 8)

10. y - 6 = 3 (x - 1 −

3 ) 11. y + 4 = -2(x + 5) 12. y + 5 −

3 = 1 −

2 (x - 2)

Example 1 Example 2

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Skills PracticeWriting Equations in Point-Slope Form

Write an equation in point-slope form for the line that passes through each point with the given slope.

1.

(–1, –2)x

y

O

m = 3

2.

(1, –2)x

y

O

m = –1 3.

(2, –3)

x

y

O

m = 0

4. (3, 1), m = 0 5. (-4, 6), m = 8 6. (1, -3), m = -4

7. (4, -6), m = 1 8. (3, 3), m = 4 −

3 9. (-5, -1), m = -

5 −

4

Write each equation in standard form.

10. y + 1 = x + 2 11. y + 9 = -3(x - 2) 12. y - 7 = 4(x + 4)

13. y - 4 = -(x - 1) 14. y - 6 = 4(x + 3) 15. y + 5 = -5(x - 3)

16. y - 10 = -2(x - 3) 17. y - 2 = -

1 −

2 (x - 4) 18. y + 11 = 1 −

3 (x + 3)


19. y - 4 = 3(x - 2) 20. y + 2 = -(x + 4) 21. y - 6 = -2(x + 2)

22. y + 1 = -5(x - 3) 23. y - 3 = 6(x - 1) 24. y - 8 = 3(x + 5)

25. y - 2 = 1 −

2 (x + 6) 26. y + 1 = -

1 −

3 (x + 9) 27. y - 1 −

2 = x + 1 −

2

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PracticeWriting Equations in Point-Slope Form

Write an equation in point-slope form for the line that passes through each point with the given slope.

1. (2, 2), m = -3 2. (1, -6), m = -1 3. (-3, -4), m = 0

4. (1, 3), m = -

3 −

4 5. (-8, 5), m = -

2 −

5 6. (3, -3), m = 1 −

3

Write each equation in standard form.

7. y - 11 = 3(x - 2) 8. y - 10 = -(x - 2) 9. y + 7 = 2(x + 5)

10. y - 5 = 3 −

2 (x + 4) 11. y + 2 = -

3 −

4 (x + 1) 12. y - 6 = 4 −

3 (x - 3)

13. y + 4 = 1.5(x + 2) 14. y - 3 = -2.4(x - 5) 15. y - 4 = 2.5(x + 3)


16. y + 2 = 4(x + 2) 17. y + 1 = -7(x + 1) 18. y - 3 = -5(x + 12)

19. y - 5 = 3 −

2 (x + 4) 20. y - 1 −

4 = - 3 (x + 1 −

4 ) 21. y - 2 −

3 = -2 (x - 1 −

4 )

22. CONSTRUCTION A construction company charges $15 per hour for debris removal, plus a one-time fee for the use of a trash dumpster. The total fee for 9 hours of service is $195.

a. Write the point-slope form of an equation to find the total fee y for any number of hours x.

b. Write the equation in slope-intercept form.

c. What is the fee for the use of a trash dumpster?

23. MOVING There is a daily fee for renting a moving truck, plus a charge of $0.50 per mile driven. It costs $64 to rent the truck on a day when it is driven 48 miles.

a. Write the point-slope form of an equation to find the total charge y for a one-day rental with x miles driven.

b. Write the equation in slope-intercept form.

c. What is the daily fee?

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1. BICYCLING Harvey rides his bike at an average speed of 12 miles per hour. In other words, he rides 12 miles in 1 hour, 24 miles in 2 hours, and so on. Let h be the number of hours he rides and d be distance traveled. Write an equation for the relationship between distance and time in point-slope form.

2. GEOMETRY The perimeter of a square varies directly with its side length. The point-slope form of the equation for this function is y - 4 = 4(x - 1). Write the equation in standard form.

3. NATURE The frequency of a male cricket’s chirp is related to the outdoor temperature. The relationship is expressed by the equation T = n + 40, where T is the temperature in degrees Fahrenheit and n is the number of chirps the cricket makes in 14 seconds. Use the information from the graph below to write an equation for the line in point-slope form .

Number of Chirps151050 2520

y

x30 35

Tem

per

atu

re (

°F)

30

40

20

10

50

70

60

4. CANOEING Geoff paddles his canoe at an average speed of 3.5 miles per hour. After 5 hours of canoeing, Geoff has traveled 18 miles. Write an equation in point-slope form to find the total distance y for any number of hours x.

5. AVIATION A jet plane takes off and consistently climbs 20 feet for every 40 feet it moves horizontally. The graph shows the trajectory of the jet.

Horizontal Distance (ft)

5000 1000 1500 2000 2500

Hei

gh

t (f

t)600

800

400

200

1000

1400

1200

a. Write an equation in point-slope form for the line representing the jet’s trajectory.

b. Write the equation from part a in slope -intercept form.

c. Write the equation in standard form.

Word Problem PracticeWriting Equations in Point-Slope Form

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Enrichment

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y

O

x

y

O

Collinearity You have learned how to find the slope between two points on a line. Does it matter which two points you use? How does your choice of points affect the slope-intercept form of the equation of the line?

1. Choose three different pairs of points from the graph at the right. Write the slope-intercept form of the line using each pair.

2. How are the equations related?

3. What conclusion can you draw from your answers to Exercises 1 and 2?

When points are contained in the same line, they are said to be collinear. Even though points may look like they form a line when connected, it doesnot mean that they actually do. By checking pairs of points on a graph you can determine whether the graph represents a linear relationship.

4. Choose several pairs of points from the graph at the right and write the slope-intercept form of the line containingeach pair.

5. What conclusion can you draw from your equations in Exercise 4? Is this a line?

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Graphing Calculator ActivityWriting Linear Equations

Lists can be used with the linear regression function to write and verify linear equations given two points on a line, or the slope of a line and a point through which it passes. The linear regression function, LinReg (ax + b), is found under the STAT CALC menu.

Write the slope-intercept form of an equation of the line that passes through (3, -2) and (6, 4).

Enter the x-coordinates of the points into L1 and the y-coordinates into L2. Use the linear regression function to write the equation of the line.

Keystrokes: STAT ENTER 3 ENTER 6 ENTER (–) 2 ENTER 4 ENTER STAT 4 2nd [L1] , 2nd [L2] ENTER .

The equation is y = 2x - 8.

If you have already written the equation of a line, you can use the given information to verify your equation.

ExercisesWrite the slope-intercept form and the standard form of an equation of the line that satisfies each condition.

1. passes through (0, 7) and ( 1 −

7 , -5) 2. passes through (-5, 1), (10, 10), and (-10, -2)

3. passes through (6, -4), m = 2 −

3 4. passes through (3, 5), m = -4

5. x-intercept: 1, y-intercept: -

1 −

2 6. passes through (-18, 11), y-intercept: 3

Verify that the equation of the line passing through (2, -3) with slope -

3 −

4 can be written as 3x + 4y = -6.

Use the given point and slope to determine a second point through which the line passes. Enter the x-coordinates of the points into L1 and the y-coordinates into L2. Use LinReg (ax + b) to determine the slope-intercept form of the equation.

The slope-intercept form of the equation is y = -0.75x - 1.5 or y = -

3 −

4 x - 3 −

2 .

This can be rewritten in standard form as 3x + 4y = -6.

Example 1

Example 2

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Study Guide and InterventionParallel and Perpendicular Lines

Parallel Lines Two nonvertical lines are parallel if they have the same slope. All vertical lines are parallel.

Write an equation in slope-intercept form for the line that passes through (-1, 6) and is parallel to the graph of y = 2x + 12.

A line parallel to y = 2x + 12 has the same slope, 2. Replace m with 2 and (x1, y1) with (-1, 6) in the point-slope form. y - y1 = m(x - x1) Point-slope form

y - 6 = 2(x - (-1)) m = 2; (x1, y

1) = (-1, 6)

y - 6 = 2(x + 1) Simplify.

y - 6 = 2x + 2 Distributive Property

y = 2x + 8 Slope-intercept form

Therefore, the equation is y = 2x + 8.

ExercisesWrite an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of each equation.

1. 2. 3.

4. (-2, 2), y = 4x - 2 5. (6, 4), y = 1 −

3 x + 1 6. (4, -2), y = -2x + 3

7. (-2, 4), y = -3x + 10 8. (-1, 6), 3x + y = 12 9. (4, -6), x + 2y = 5

10. Find an equation of the line that has a y-intercept of 2 that is parallel to the graph of the line 4x + 2y = 8.

11. Find an equation of the line that has a y-intercept of -1 that is parallel to the graph of the line x - 3y = 6.

12. Find an equation of the line that has a y-intercept of -4 that is parallel to the graph of the line y = 6.

(–3, 3)

x

y

O

4x - 3y = –12

(-8, 7)

x

y

O

y = - x - 412

2

2

(5, 1)x

y

O

y = x - 8

Example

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Parallel and Perpendicular Lines

Perpendicular Lines Two nonvertical lines are perpendicular if their slopes are negative reciprocals of each other. Vertical and horizontal lines are perpendicular.

Write an equation in slope-intercept form for the line that passes through (-4, 2) and is perpendicular to the graph of 2x - 3y = 9.

Find the slope of 2x - 3y = 9. 2x - 3y = 9 Original equation

-3y = -2x + 9 Subtract 2x from each side.

y = 2 −

3 x - 3 Divide each side by -3.

The slope of y = 2 −

3 x - 3 is 2 −

3 . So, the slope of the line passing through (-4, 2) that is

perpendicular to this line is the negative reciprocal of 2 −

3 , or -

3 −

2 .

Use the point-slope form to find the equation.y - y1 = m(x - x1) Point-slope form

y - 2 = -

3 −

2 (x - (-4)) m = -

3 −

2 ; (x

1, y

1) = (-4, 2)

y - 2 = -

3 −

2 (x + 4) Simplify.

y - 2 = -

3 −

2 x - 6 Distributive Property

y = -

3 −

2 x - 4 Slope-intercept form

Exercises 1. ARCHITECTURE On the architect’s plans for a new high school, a wall represented

by −−−

MN has endpoints M(-3, -1) and N(2, 1). A wall represented by −−−

PQ has endpoints P(4, -4) and Q(-2, 11). Are the walls perpendicular? Explain.

Determine whether the graphs of the following equations are parallel or perpendicular.

2. 2x + y = -7, x - 2y = -4, 4x - y = 5

3. y = 3x, 6x - 2y = 7, 3y = 9x - 1

Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of each equation.

4. (4, 2), y = 1 −

2 x + 1 5. (2, -3), y = -

2 −

3 x + 4 6. (6, 4), y = 7x + 1

7. (-8, -7), y = -x - 8 8. (6, -2), y = -3x - 6 9. (-5, -1), y = 5 −

2 x - 3

Example

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Skills PracticeParallel and Perpendicular Lines

Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the given equation.

1. 2. 3.

4. (3, 2), y = 3x + 4 5. (-1, -2), y = -3x + 5 6. (-1, 1), y = x - 4

7. (1, -3), y = -4x - 1 8. (-4, 2), y = x + 3 9. (-4, 3), y = 1 −

2 x - 6

10. RADAR On a radar screen, a plane located at A(-2, 4) is flying toward B(4, 3).

Another plane, located at C(-3, 1), is flying toward D(3, 0). Are the planes’ paths perpendicular? Explain.

Determine whether the graphs of the following equations are parallel or perpendicular. Explain.

11. y = 2 −

3 x + 3, y = 3 −

2 x, 2x - 3y = 8

12. y = 4x, x + 4 y = 12, 4x + y = 1

Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the given equation.

13. (-3, -2), y = x + 2 14. (4, -1), y = 2x - 4 15. (-1, -6), x + 3y = 6

16. (-4, 5), y = -4x - 1 17. (-2, 3), y =

1 −

4 x - 4 18. (0, 0), y =

1 −

2 x - 1

(–2, 2)

x

y

O

y = 12 x + 1(1, –1)

x

y

O

y = –x + 3

(–2, –3)

x

y

O

y = 2x - 1

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Practice Parallel and Perpendicular Lines

Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the given equation.

1. (3, 2), y = x + 5 2. (-2, 5), y = -4x + 2 3. (4, -6), y = -

3

−

4

x + 1

4. (5, 4), y = 2 −

5 x - 2 5. (12, 3), y = 4 −

3 x + 5 6. (3, 1), 2x + y = 5

7. (-3, 4), 3y = 2x - 3 8. (-1, -2), 3x - y = 5 9. (-8, 2), 5x - 4y = 1

10. (-1, -4), 9x + 3y = 8 11. (-5, 6), 4x + 3y = 1 12. (3, 1), 2x + 5y = 7

Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the given equation.

13. (-2, -2), y = -

1

−

3

x + 9 14. (-6, 5), x - y = 5 15. (-4, -3), 4x + y = 7

16. (0, 1), x + 5y = 15 17. (2, 4), x - 6y = 2 18. (-1, -7), 3x + 12y = -6

19. (-4, 1), 4x + 7y = 6 20. (10, 5), 5x + 4y = 8 21. (4, -5), 2x - 5y = -10

22. (1, 1), 3x + 2y = -7 23. (-6, -5), 4x + 3y = -6 24. (-3, 5), 5x - 6y = 9

25. GEOMETRY Quadrilateral ABCD has diagonals −−

AC and −−−

BD . Determine whether

−−

AC is perpendicular to −−−

BD . Explain.

26. GEOMETRY Triangle ABC has vertices A(0, 4), B(1, 2), and C(4, 6). Determine whether triangle ABC is a right triangle. Explain.

x

y

O

A

D

C

B

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1. BUSINESS Brady’s Books is a retail store. The store’s average daily profits y are given by the equation y = 2x + 3 where x is the number of hours available for customer purchases. Brady’s adds an online shopping option. Write an equation in slope-intercept form to show a new profit line with the same profit rate containing the point (0, 12).

2. ARCHITECTURE The front view of a house is drawn on graph paper. The left side of the roof of the house is represented by the equation y = x. The rooflines intersect at a right angle and the peak of the roof is represented by the point (5, 5). Write the equation in slope-intercept form for the line that creates the right side of the roof.

3. ARCHAEOLOGY An archaeologist is comparing the location of a jeweled box she just found to the location of a brick wall. The wall can be represented by the

equation y = -

5 −

3 x + 13. The box is

located at the point (10, 9). Write an equation representing a line that is perpendicular to the wall and that passes through the location of the box.

4. GEOMETRY A parallelogram is created by the intersections of the lines x = 2,

x = 6, y = 1 −

2 x + 2, and another line. Find

the equation of the fourth line needed to complete the parallelogram. The line should pass through (2, 0). (Hint: Sketch a graph to help you see the lines.)

5. INTERIOR DESIGN Pamela is planning to install an island in her kitchen. She draws the shape she likes by connecting the vertices of the square tiles on her kitchen floor. She records the location of each corner in the table.

a. How many pairs of parallel sides are there in the shape ABCD she designed? Explain.

b. How many pairs of perpendicular sides are there in the shape she designed? Explain.

c. What is the shape of her new island?

Word Problem PracticeParallel and Perpendicular Lines

y

xO

(5, 5)

Corner

Distance

from West

Wall (tiles)

Distance

from South

Wall (tiles)

A 5 4

B 3 8

C 7 10

D 11 7

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Enrichment

Pencils of LinesAll of the lines that pass through a single point in the same plane are called a pencil of lines.All lines with the same slope, but different intercepts, are also called a “pencil,” a pencil of parallel lines.

Graph some of the lines in each pencil.

1. A pencil of lines through the 2. A pencil of lines described by point (1, 3) y - 4 = m(x - 2), where m is any

real number

3. A pencil of lines parallel to the line 4. A pencil of lines described by x - 2y = 7 y = mx + 3m - 2 , where m is any

real number

x

y

Ox

y

O

x

y

Ox

y

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Study Guide and InterventionScatter Plots and Lines of Fit

Investigate Relationships Using Scatter Plots A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane. If y increases as x increases, there is a positive correlation between x and y. If y decreases as x increases, there is a negative correlation between x and y. If x and y are not related, there is no correlation.

EARNINGS The graph at the right shows the amount of money Carmen earned each week and the amount she deposited in her savings account that same week. Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.

The graph shows a positive correlation. The more Carmen earns, the more she saves.

ExercisesDetermine whether each graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.

1. 2.

3. 4.

Average Weekly Work Hours in U.S.

Hour

s

34.0

34.2

33.8

33.6

34.4

34.6

Years Since 19953210 54 76 98

Source: The World Almanac

Average Jogging Speed

Minutes

Mile

s pe

r Hou

r

0 10 205 15 25

10

5

Carmen’s Earnings and Savings

Dollars Earned

Dolla

rs S

aved

0 40 80 120

35

30

25

20

15

10

5

Example

Average U.S. HourlyEarnings

Hour

ly E

arni

ngs

($)

15

0

16

17

18

19

Years Since 2003Source: U.S. Dept. of Labor

1 2 3 4 5

U.S. Imports from Mexico

Impo

rts

($ b

illio

ns)

130

0

160

190

220

Years Since 2003Source: U.S. Census Bureau

1 2 3 4 5

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Use Lines of Fit

The table shows the number of students per computer in Easton High School for certain school years from 1996 to 2008.

Year 1996 1998 2000 2002 2004 2006 2008

Students per Computer 22 18 14 10 6.1 5.4 4.9

a. Draw a scatter plot and determine what relationship exists, if any.Since y decreases as x increases, the correlation is negative.

b. Draw a line of fit for the scatter plot.Draw a line that passes close to most of the points. A line of fit is shown.

c. Write the slope-intercept form of an equation for the line of fit.The line of fit shown passes through (1999, 16) and (2005, 5.7). Find the slope.

m = 5.7 - 16

−

2005 - 1999

m = -1.7 Find b in y = -1.7x + b. 16 = -1.7 · 1993 + b 3404 = b Therefore, an equation of a line of fit is y = -1.7x + 3404.

ExercisesRefer to the table for Exercises 1–3.

1. Draw a scatter plot.

2. Draw a line of fit for the data.

3. Write the slope-interceptform of an equation for the line of fit.

Movie Admission Prices

Adm

issi

on ($

)

5.4

5.6

5.2

5

5.8

6

6.2

Years Since 19993210 54

Source: U.S. Census Bureau


Scatter Plots and Lines of Fit

Students per Computerin Easton High School

Stud

ents

per

Com

pute

r

81216

4

0

2024

Year1996 1998 2000 2002 2004 2006 2008

Example

Years

Since 1999

Admission

(dollars)

0 $5.08

1 $5.39

2 $5.66

3 $5.81

4 $6.03

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Skills PracticeScatter Plots and Lines of Fit

Determine whether each graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.

1. 2.

3. 4.

5. BASEBALL The scatter plot shows the average price of a major-league baseball ticket from 1997 to 2006.

a. Determine what relationship, if any, exists in the data. Explain.

b. Use the points (1998, 13.60) and (2003, 19.00) to write the slope-intercept form of an equation for the line of fit shown in the scatter plot.

c. Predict the price of a ticket in 2009.

Weight-Lifting

Weight (pounds)

Repe

titio

ns

0 40 8020 60 100 120 140

14

12

10

8

6

4

2

Library Fines

Books Borrowed

Fine

s (d

olla

rs)

0 2 4 5 6 7 8 91 3 10

7

6

5

4

3

2

1

Calories BurnedDuring Exercise

Time (minutes)

Calo

ries

0 20 4010 30 50 60

600

500

400

300

200

100

Baseball Ticket Prices

Aver

age

Pric

e ($

)

14

16

12

0

18

20

22

24

Year’99’98’97 ’01 ’03’00

Source: Team Marketing Report, Chicago

’02 ’04 ’05 ’06

Car Dealership Revenue

Reve

nue

(hun

dred

s of

thou

sand

s)

4

6

2

0

8

10

12

14

Year’99 ’01 ’03’00 ’02 ’04 ’05 ’06 ’07 ’08

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Practice Scatter Plots and Lines of Fit

Determine whether each graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.

1. 2.

3. DISEASE The table shows the number of cases of Foodborne Botulism in the United States for the years 2001 to 2005.

a. Draw a scatter plot and determine what relationship, if any, exists in the data.

b. Draw a line of fit for the scatter plot.

c. Write the slope-intercept form of an equation for the

line of fit.

4. ZOOS The table shows the average and maximum longevity of various animals in captivity.


b. Draw a line of fit for the scatter plot.

c. Write the slope-intercept form of an equation for the line of fit.

d. Predict the maximum longevity for an animal with an average longevity of 33 years.

State Elevations

Mean Elevation (feet)

High

est P

oint

(thou

sand

s of

feet

)

10000 2000 3000

16

12

8

4

Source: U.S. Geological Survey

Temperature versus Rainfall

Average Annual Rainfall (inches)

Aver

age

Tem

pera

ture

(ºF)

10 15 20 25 30 35 40 45

64

60

56

52

0

Source: National Oceanic and AtmosphericAdministration

U.S. FoodborneBotulism Cases

Case

s

20

30

10

0

40

50

Year2001 2002 2003 2004 2005

Animal Longevity (Years)

Average

Max

imum

50 10 15 20 25 30 35 40 45

80

70

60

50

40

30

20

10

Source: Centers for Disease Control

U.S. Foodborne Botulism Cases

Year 2001 2002 2003 2004 2005

Cases 39 28 20 16 18

Source: Walker’s Mammals of the World

Longevity (years)

Avg. 12 25 15 8 35 40 41 20

Max. 47 50 40 20 70 77 61 54

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1. MUSIC The scatter plot shows the number of CDs in millions that were sold from 1999 to 2005. If the trend continued, about how many CDs were sold in 2006?

2. FAMILY The table shows the predicted annual cost for a middle income family to raise a child from birth until adulthood. Draw a scatter plot and describe what relationship exists within the data.

3. HOUSING The median price of an existing home was $160,000 in 2000 and $240,000 in 2007. If x represents the number of years since 2000, use these data points to determine a line of best fit for the trends in the price of existing homes. Write the equation in slope-intercept form.

4. BASEBALL The table shows the average length in minutes of professional baseball games in selected years.

Source: Elias Sports Bureau


b. Explain what the scatter plot shows.

c. Draw a line of fit for the scatter plot.

Tim

e (m

in)

166

0

168

170

172

174

176

178

180

Year’90 ’92 ’94 ’96 ’98 ’00 ’02

Age (years)30 6 12 15

y

x9

An

nu

al C

ost

($1

000)

11

12

10

9

13

16

15

14

17

Source: The World Almanac

Source: RIAA

Year‘01‘00‘990 ‘03‘02 ‘05

y

x‘04

CD

s (m

illio

ns)

750

800

700

650

850

950

900

Word Problem PracticeScatter Plots and Lines of Fit

Cost of Raising a Child Born in 2003

Child’s

Age3 6 9 12 15

Annual

Cost ($)10,700 11,700 12,600 15,000 16,700

Average Length of

Major League Baseball Games

Year ‘92 ‘94 ‘96 ‘98 ‘00 ‘02 ‘04

Time (min) 170 174 171 168 178 172 167

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Enrichment

Latitude and Temperature

The latitude of a place on Earth is the measure of its distance fromthe equator. What do you think is the relationship between a city’s latitude and its mean January temperature? At the right is a table containing the latitudes and January mean temperatures for fifteen U.S. cities.

Sources: National Weather Service

1. Use the information in the table to create a scatter plot and draw a line of best fit for the data.

2. Write an equation for the line of fit. Make a conjecture about the relationship between a city’s latitude and its mean January temperature.

3. Use your equation to predict the January mean temperature of Juneau, Alaska, which has latitude 58:23 N.

4. What would you expect to be the latitude of a city with a January mean temperature of 15°F?

5. Was your conjecture about the relationship between latitude and temperature correct?

6. Research the latitudes and temperatures for cities in the southern hemisphere. Does your conjecture hold for these cities as well?

Latitude (ºN)

Tem

per

atu

re (

ºF)

70

60

50

40

30

20

10

0

-10

T

L20 40 6010 30 50

U.S. City Latitude January Mean Temperature

Albany, New York 42:40 N 20.7°F

Albuquerque, New Mexico 35:07 N 34.3°F

Anchorage, Alaska 61:11 N 14.9°F

Birmingham, Alabama 33:32 N 41.7°F

Charleston, South Carolina 32:47 N 47.1°F

Chicago, Illinois 41:50 N 21.0°F

Columbus, Ohio 39:59 N 26.3°F

Duluth, Minnesota 46:47 N 7.0°F

Fairbanks, Alaska 64:50 N -10.1°F

Galveston, Texas 29:14 N 52.9°F

Honolulu, Hawaii 21:19 N 72.9°F

Las Vegas, Nevada 36:12 N 45.1°F

Miami, Florida 25:47 N 67.3°F

Richmond, Virginia 37:32 N 35.8°F

Tucson, Arizona 32:12 N 51.3°F

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ExercisesThe table shows the number of millions of dollars of direct political contributions received by Democrats and Republicansin selected years.1. Use a spreadsheet to draw a scatter plot and a trendline for the

data. Let x represent the number of years since 1990 and let y represent direct political contributions in millions of dollars.

2. Predict the amount of direct political contributions for the 2010 election.

Spreadsheet ActivityScatter Plots

The table below shows the number of metric tons of gold produced in mines in the United States in selected years.

Use a spreadsheet to draw a scatter plot and a trendline for the data. Let x represent the number of years since 2000 and let y represent the number of metric tons of gold. Then predict the number of ounces of gold produced in 2013.

Step 1 Use Column A for the years since 2000 and Column B for the number of metric tons of gold. To create a graph from the data, select the data in Columns A and B and choose Chart from the Insert menu. Select an XY (Scatter) chart to show the data points.

Step 2 Add a trendline to the graph by choosing the Chart menu. Add a linear trendline. Use the options menu to have the trendline forecast 5 years forward.

Using this trendline, it appears that the gold production for 2013 will be approximately 150 metric tons.

A spreadsheet program can create scatter plots of data that you enter. You can also have the spreadsheet graph a line of fit, called a trendline, automatically.

Example

Source: Open Secrets

Year Contributions

1990 281

1994 337

1998 445

2002 717

2006 1085

Source: U.S. Geological Survey

Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Gold 353 335 298 277 247 256 252 238 233 210

4-5

A1 0

12

34

5

6

78

9

353335298

277247

256

252

238233

210

34567891011121314

2

B C D E F G H

15

Spreadsheet sample

Sheet 1 Sheet 2 Sheet 3

U.S. Gold Mine Production

Gold

(met

ric to

ns)

100

150

50

0

200

250

300

350

400

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Equations of Best-Fit Lines Many graphing calculators utilize an algorithm called linear regression to find a precise line of fit called the best-fit line. The calculator computes the data, writes an equation, and gives you the correlation coefficent, a measure of how closely the equation models the data.

GAS PRICES The table shows the price of a gallon of regular gasoline at a station in Los Angeles, California on January 1 of various years. Year 2005 2006 2007 2008 2009 2010

Average Price $1.47 $1.82 $2.15 $2.49 $2.83 $3.04

Source: U.S. Department of Energy

a. Use a graphing calculator to write an equation for the best-fit line for that data. Enter the data by pressing STAT and selecting the Edit option. Let the year 2005 be represented by 0. Enter the years since 2005 into List 1 (L1). Enter the average price into List 2 (L2).

Then, perform the linear regression by pressing STAT and selecting the CALC option. Scroll down to LinReg (ax+b) and press ENTER . The best-fit equation for the regression is shown to be y = 0.321x + 1.499.

b. Name the correlation coefficient. The correlation coefficient is the value shown for r on the calculator screen. The correlation coefficient is about 0.998.

ExercisesWrite an equation of the regression line for the data in each table below. Then find the correlation coefficient.

1. OLYMPICS Below is a table showing the number of gold medals won by the United States at the Winter Olympics during various years.

Year 1992 1994 1998 2002 2006 2010

Gold Medals 5 6 6 10 9 9

Source: International Olympic Committee

2. INTEREST RATES Below is a table showing the U.S. Federal Reserve’s prime interest rate on January 1 of various years.

Year 2006 2007 2008 2009 2010

Prime Rate (percent) 7.25 8.25 7.25 3.25 3.25

Source: Federal Reserve Board

Study Guide and InterventionRegression and Median-Fit Lines

Example

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Equations of Median-Fit Lines A graphing calculator can also find another type of best-fit line called the median-fit line, which is found using the medians of the coordinates of the data points.

ELECTIONS The table shows the total number of people in millions who voted in the U.S. Presidential election in the given years.

Year 1980 1984 1988 1992 1996 2004 2008

Voters 86.5 92.7 91.6 104.4 96.3 122.3 131.3

Source: George Mason University

a. Find an equation for the median-fit line. Enter the data by pressing STAT and selecting the Edit option. Let the year 1980 be represented by 0. Enter the years since 1980 into List 1 (L1). Enter the number of voters into List 2 (L2).

Then, press STAT and select the CALC option. Scroll down to Med-Med option and press ENTER . The value of a is the slope, and the value of b is the y-intercept.The equation for the median-fit line is y = 1.55x + 83.57.

b. Estimate the number of people who voted in the 2000 U.S. Presidential election. Graph the best-fit line. Then use the

TRACE feature and the arrow keys until you find a point where x = 20.

When x = 20, y ≈ 115. Therefore, about 115 million people voted in the 2000 U.S. Presidential election.

ExercisesWrite an equation of the regression line for the data in each table below. Then find the correlation coefficient.

1. POPULATION GROWTH Below is a table showing the estimated population of Arizona in millions on July 1st of various years.

Year 2001 2002 2003 2004 2005 2006

Population 5.30 5.44 5.58 5.74 5.94 6.17


a. Find an equation for the median-fit line.

b. Predict the population of Arizona in 2009.

2. ENROLLMENT Below is a table showing the number of students enrolled at Happy Days Preschool in the given years.

Year 2002 2004 2006 2008 2010

Students 130 168 184 201 234


b. Estimate how many students were enrolled in 2007.


Regression and Median-Fit Lines

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Write an equation of the regression line for the data in each table below. Then find the correlation coefficient.

1. SOCCER The table shows the number of goals a soccer team scored each season since 2005.

Year 2005 2006 2007 2008 2009 2010

Goals Scored 42 48 46 50 52 48

2. PHYSICAL FITNESS The table shows the percentage of seventh grade students in public school who met all six of California’s physical fitness standards each year since 2002.

Year 2002 2003 2004 2005 2006

Percentage 24.0% 36.4% 38.0% 40.8% 37.5%

Source: California Department of Education

3. TAXES The table shows the estimated sales tax revenues, in billions of dollars, for Massachusetts each year since 2004.

Year 2004 2005 2006 2007 2008

Tax Revenue 3.75 3.89 4.00 4.17 4.47

Source: Beacon Hill Institute

4. PURCHASING The SureSave supermarket chain closely monitors how many diapers are sold each year so that they can reasonably predict how many diapers will be sold in the following year.

Year 2006 2007 2008 2009 2010

Diapers Sold 60,200 65,000 66,300 65,200 70,600


b. How many diapers should SureSave anticipate selling in 2011?

5. FARMING Some crops, such as barley, are very sensitive to how acidic the soil is. To determine the ideal level of acidity, a farmer measured how many bushels of barley he harvests in different fields with varying acidity levels.

Soil Acidity (pH) 5.7 6.2 6.6 6.8 7.1

Bushels Harvested 3 20 48 61 73

a. Find an equation for the regression line.

b. According to the equation, how many bushels would the farmer harvest if the soil had a pH of 10?

c. Is this a reasonable prediction? Explain.

Skills PracticeRegression and Median-Fit Lines

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Write an equation of the regression line for the data in each table below. Then find the correlation coefficient.

1. TURTLES The table shows the number of turtles hatched at a zoo each year since 2006.

Year 2006 2007 2008 2009 2010

Turtles Hatched 21 17 16 16 14

2. SCHOOL LUNCHES The table shows the percentage of students receiving free or reduced price school lunches at a certain school each year since 2006.

Year 2006 2007 2008 2009 2010

Percentage 14.4% 15.8% 18.3% 18.6% 20.9%

Source: KidsData

3. SPORTS Below is a table showing the number of students signed up to play lacrosse after school in each age group.

Age 13 14 15 16 17

Lacrosse Players 17 14 6 9 12

4. LANGUAGE The State of California keeps track of how many millions of students are learning English as a second language each year.

Year 2003 2004 2005 2006 2007

English Learners 1.600 1.599 1.592 1.570 1.569

Source: California Department of Education


b. Predict the number of students who were learning English in California in 2001.

c. Predict the number of students who were learning English in California in 2010.

5. POPULATION Detroit, Michigan, like a number of large cities, is losing population every year. Below is a table showing the population of Detroit each decade.

Year 1960 1970 1980 1990 2000

Population (millions) 1.67 1.51 1.20 1.03 0.95


a. Find an equation for the regression line.

b. Find the correlation coefficient and explain the meaning of its sign.

c. Estimate the population of Detroit in 2008.

PracticeRegression and Median-Fit Lines

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Word Problem PracticeRegression and Median-Fit Lines

1. FOOTBALL Rutgers University running back Ray Rice ran for 1732 total yards in the 2007 regular season. The table below shows his cumulative total number of yards ran after select games.

Game

Number1 3 6 9 12

Cumulative

Yards184 431 818 1257 1732

Source: Rutgers University Athletics

Use a calculator to find an equation for the regression line showing the total yards y scored after x games. What is the real-world meaning of the value returned for a?

2. GOLD Ounces of gold are traded by large investment banks in commodity exchanges much the same way that shares of stock are traded. The table below shows the cost of a single ounce of gold on the last day of trading in given years.

Year 2002 2003 2004 2005 2006

Price $346.70 $414.80 $438.10 $517.20 $636.30

Source: Global Financial Data

Use a calculator to find an equation for the regression line. Then predict the price of an ounce of gold on the last day of trading in 2009. Is this a reasonable prediction? Explain.

3. GOLF SCORES Emmanuel is practicing golf as part of his school’s golf team. Each week he plays a full round of golf and records his total score. His scorecard after five weeks is below.

Week 1 2 3 4 5

Golf Score 112 107 108 104 98

Use a calculator to find an equation for the median-fit line. Then estimate how many games Emmanuel will have to play to get a score of 86.

4. STUDENT ELECTIONS The vote totals for five of the candidates participating in Montvale High School’s student council elections and the number of hours each candidate spent campaigning are shown in the table below.

Hours

Campaigning1 3 4 6 8

Votes Received 9 22 24 46 78

a. Use a calculator to find an equation for the median-fit line.

b. Plot the data points and draw the median-fit line on the graph below.

Vote

s Re

ceiv

ed

20

30

10

0

40

50

60

70

80

Campaign Time (h)321 5 74 6 8 x

y

c. Suppose a sixth candidate spends 7 hours campaigning. Estimate how many votes that candidate could expect to receive.

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For some sets of data, a linear equation in the form y = ax + b does not adequately describe the relationship between data points. The “QuadReg” function on a graphing calculator will output an equation in the form y = ax2 + bx + c. The value of R2, the coefficient of determination tells you how closely the parabola fits the data.

The table shows the population of Atlanta in various years.

Year 1970 1980 1990 2000 2005 2007

Population 497,000 425,000 394,017 416,474 470,688 498,109


a. Find the equation of a quadratic-regression parabola for the data.

Running a linear regression on the data provides an r value of 0.03, which indicates a poor fit. The data appears to be a good candidate for a quadratic regression.

Step 1 Enter the data by pressing STAT and selecting the Edit option. Enter the years since 1970 as your x-values (L1) and enter the population figures as your y-values (L2).

Step 2 Perform the quadratic regression by pressing STAT and selecting the CALC option. Scroll down to QuadReg and press ENTER .

Step 3 Write the equation of the best-fit parabola by rounding the a, b, and c values on the screen.The equation for the best-fit parabola is y = 302.8x2 – 11,480x + 501,227.

b. Find the coefficient of determination.

The coefficient of determination for the parabola is R2 = 0.969, which indicates a good fit.

c. Use the quadratic-regression parabola to predict the population in 2010.

Graph the best-fit parabola. Then use the TRACE feature and the arrow keys until you find a point where x = 40.When x ≈ 40, y ≈ 525,000. The estimated population will be 525,000.

Exercises

1. The table below shows the average high temperature in Crystal River, Florida in various months.

Month Jan (1) Mar (3) May (5) Jul (7) Sep (9) Nov (11)

Avg. High (°F) 68° 76° 87° 91° 88° 76°

Source: Country Studies

a. Find the equation of the best-fit parabola.

b. Find the coefficient of determination.

c. Use the quadratic-regression parabola to predict the average high temperature in April (4th month).

EnrichmentQuadratic Regression Parabolas

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Inverse Relations An inverse relation is the set of ordered pairs obtained by exchanging the x-coordinates with the y-coordinates of each ordered pair. The domain of a relation becomes the range of its inverse, and the range of the relation becomes the domain of its inverse.

Find and graph the inverse of the relation represented by line a.The graph of the relation passes through (–2, –10), (–1, –7), (0, –4), (1, –1), (2, 2), (3, 5), and (4, 8).

To find the inverse, exchange the coordinates of the ordered pairs.

The graph of the inverse passes through the points (–10, –2), (–7, –1), (–4, 0), (–1, 1), (2, 2), (5, 3), and (8, 4). Graph these points and then draw the line that passes through them.

ExercisesFind the inverse of each relation.

1. {(4, 7), (6, 2), (9, –1), (11, 3)} 2. {(–5, –9), (–4, –6), (–2, –4), (0, –3)}

3. x y

–8 –15

–2 –11

1 –8

5 1

11 8

4. x y

–8 3

–2 9

2 13

6 18

8 19

5. x y

–6 14

–5 11

–4 8

–3 5

–2 2

Graph the inverse of each relation.

6. y

xO

8

4

−4−8 4 8

−4

−8

7. y

xO

8

4

−4−8 4 8

−4

−8

8. y

xO

8

4

−4−8 4 8

−4

−8

Study GuideInverse Linear Functions

Example

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−4−8 4 8

−4

−8

(−10, −2)

(−4, 0) (2, 2)

(8, 4)

a

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Study Guide (continued)

Inverse Linear Functions

Inverse Functions A linear relation that is described by a function has an inverse function that can generate ordered pairs of the inverse relation. The inverse of the linear function f (x) can be written as f -1 (x) and is read f of x inverse or the inverse of f of x.

Find the inverse of f (x) = 3 −

4 x + 6.

Step 1 f (x) = 3 −

4 x + 6 Original equation

y = 3 −

4 x + 6 Replace f (x) with y.

Step 2 x = 3 −

4 y + 6 Interchange y and x.

Step 3 x - 6 = 3 −

4 y Subtract 6 from each side.

4 −

3 (x - 6) = y Multiply each side by 4 −

3 .

Step 4 4 −

3 (x - 6) = f -1 (x) Replace y with f -1 (x).

The inverse of f (x) = 3 −

4 x + 6 is f -1 (x) = 4 −

3 (x - 6) or f -1 (x) = 4 −

3 x - 8.

ExercisesFind the inverse of each function.

1. f (x) = 4x - 3 2. f (x) = -3x + 7 3. f (x) = 3 −

2 x - 8

4. f (x) = 16 - 1 −

3 x 5. f (x) = 3(x - 5) 6. f (x) = -15 - 2 −

5 x

7. TOOLS Jimmy rents a chainsaw from the department store to work on his yard. The total cost C(x) in dollars is given by C(x) = 9.99 + 3.00x, where x is the number of days he rents the chainsaw.

a. Find the inverse function C -1 (x).

b. What do x and C -1 (x) represent in the context of the inverse function?

c. How many days did Jimmy rent the chainsaw if the total cost was $27.99?

Example

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Find the inverse of each relation.

1. x y

–9 –1

–7 –4

–5 –7

–3 –10

–1 –13

2. x y

1 8

2 6

3 4

4 2

5 0

3. x y

–4 –2

–2 –1

0 1

2 0

4 2

4. {(-3, 2), (-1, 8), (1, 14), (3, 20)} 5. {(5, -3), (2, -9), (-1, -15), (-4, -21)}

6. {(4, 6), (3, 1), (2, -4), (1, -9)} 7. {(-1, 16), (-2, 12), (-3, 8), (-4, 4)}

Graph the inverse of each function.

8. y

xO

8

4

−4−8 4 8

−4

−8

9. y

xO

8

4

−4−8 4 8

−4

−8

10. y

xO

8

4

−4−8 4 8

−4

−8

Find the inverse of each function.

11. f (x) = 8x - 5 12. f (x) = 6(x + 7) 13. f (x) = 3 −

4 x + 9

14. f (x) = -16 + 2 −

5 x 15. f (x) = 3x + 5 −

4 16. f (x) = -4x + 1 −

5

17. LEMONADE Chrissy spent $5.00 on supplies and lemonade powder for her lemonade stand. She charges $0.50 per glass.

a. Write a function P(x) to represent her profit per glass sold.

b. Find the inverse function, P -1 (x).

c. What do x and P -1 (x) represent in the context of the inverse function?

d. How many glasses must Chrissy sell in order to make a $3 profit?

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Find the inverse of each relation.

1. {(-2, 1), (-5, 0), (-8, -1), (-11, 2)} 2. {(3, 5), (4, 8), (5, 11), (6, 14)}

3. {(5, 11), (1, 6), (-3, 1), (-7, -4)} 4. {(0, 3), (2, 3), (4, 3), (6, 3)}

Graph the inverse of each function.

5. y

xO

8

4

−4−8 4 8

−4

−8

6. y

xO

8

4

−4−8 4 8

−4

−8

7. y

xO

8

4

−4−8 4 8

−4

−8


8. f (x) = 6 −

5 x - 3 9. f (x) = 4x + 2 −

3 10. f (x) = 3x - 1 −

6

11. f (x) = 3(3x + 4) 12. f (x) = -5(-x - 6) 13. f (x) = 2x - 3 −

7

Write the inverse of each equation in f -1 (x) notation.

13. 4x + 6y = 24 14. -3y + 5x = 18 15. x + 5y = 12

16. 5x + 8y = 40 17. -4y - 3x = 15 + 2y 18. 2x - 3 = 4x + 5y

19. CHARITY Jenny is running in a charity event. One donor is paying an initial amount of $20.00 plus an extra $5.00 for every mile that Jenny runs.

a. Write a function D(x) for the total donation for x miles run.

b. Find the inverse function, D -1 (x).

c. What do x and D -1 (x) represent in the context of the inverse function?

PracticeInverse Linear Functions

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Word Problem PracticeInverse Linear Functions

1. BUSINESS Alisha started a baking business. She spent $36 initially on supplies and can make 5 dozen brownies at a cost of $12. She charges her customers $10 per dozen brownies.

a. Write a function C(x) to represent Alisha’s total cost per dozen brownies.

b. Write a function E(x) to represent Alisha’s earnings per dozen brownies sold.

c. Find P (x) = E(x) - C(x). What does P (x) represent?

d. Find C -1 (x), E -1 (x), and P -1 (x).

e. How many dozen brownies does Alisha need to sell in order to make a profit?

2. GEOMETRY The area of the base of a cylindrical water tank is 66 square feet. The volume of water in the tank is dependent on the height of the water hand is represented by the function V(h) = 66h. Find V -1 (h). What will the height of the water be when the volume reaches 2310 cubic feet?

3. SERVICE A technician is working on a furnace. He is paid $150 per visit plus $70 for every hour he works on the furnace.

a. Write a function C(x) to represent the total charge for every hour of work.

b. Find the inverse function, C -1 (x).

c. How long did the technician work on the furnace if the total charge was $640?

4. FLOORING Kara is having baseboard installed in her basement. The total cost C(x) in dollars is given by C(x) = 125 + 16x, where x is the number of pieces of wood required for the installation.

a. Find the inverse function C -1 (x).

b. If the total cost was $269 and each piece of wood was 12 feet long, how many total feet of wood were used?

5. BOWLING Libby’s family went bowling during a holiday special. The special cost $40 for pizza, bowling shoes, and unlimited drinks. Each game cost $2. How many games did Libby bowl if the total cost was $112 and the six family members bowled an equal number of games?

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In a function, there is exactly one output for every input. In other words, every element in the domain pairs with exactly one element in the range. When a function is one-to-one, each element of the domain pairs with exactly one unique element in the range. When a function is onto, each element of the range corresponds to an element in the domain.

If a function is both one-to-one and onto, then the inverse is also a function.

Determine whether each relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither.

1. 1116

-34

369

12

2. 12345

-3-2

045

3. 369

1215

1050

-5

4. 427

116

1-2-4

7

5. 26

13

23468

6. 31

-910

24

111719

Determine whether the inverse of each function is also a function.

7. y

xO

8

4

−4−8 4 8

−4

−8

8. y

xO

8

4

−4−8 4 8

−4

−8

9. y

xO

8

4

−4−8 4 8

−4

−8

EnrichmentOne-to-One and Onto Functions

26912

-13589

one–to–one

-3-2-1

26

35

10

onto

579

10

-6-11-15-19

both

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Read each question. Then fill in the correct answer.

1. A B C D

2. F G H J

3. A B C D

4. F G H J

5. A B C D

6. F G H J

Multiple Choice

Student Recording SheetUse this recording sheet with pages 280–281 of the Student Edition.

Short Response/Gridded Response

Record your answer in the blank.

For gridded response questions, also enter your answer in the grid by writing each number or symbol in a box. Then fill in the corresponding circle for that number or symbol.

7.

8. (grid in)

9.

10a.

10b.

11a.

11b.

11c.

8.

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

. . . . .

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

Extended Response

Record your answers for Question 12 on the back of this paper.

049_059_ALG1_A_CRM_C04_AS_660499.indd 49049_059_ALG1_A_CRM_C04_AS_660499.indd 49 12/21/10 12:49 AM12/21/10 12:49 AM

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4 Rubric for Scoring Extended Response Test

General Scoring Guidelines

• If a student gives only a correct numerical answer to a problem but does not show how he or she arrived at the answer, the student will be awarded only 1 credit. All extended response questions require the student to show work.

• A fully correct answer for a multiple-part question requires correct responses for all parts of the question. For example, if a question has three parts, the correct response to one or two parts of the question that required work to be shown is not considered a fully correct response.

• Students who use trial and error to solve a problem must show their method. Merely showing that the answer checks or is correct is not considered a complete response for full credit.

Exercise 12 Rubric

Score Specifi c Criteria

4 Student explain that the slopes of the lines must be compared. If two lines have the same slope, they are parallel. If their slopes are opposite reciprocals, they are perpendicular.

3 A generally correct solution, but may contain minor flaws in reasoning or computation.

2 A partially correct interpretation and/or solution to the problem.

1 A correct solution with no evidence or explanation.

0 An incorrect solution indicating no mathematical understanding of the concept or task, or no solution is given.


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4

4

SCORE

For Questions 1 and 2, write an equation in slope-intercept form for each situation.

1. slope: 1 −

4 , y-intercept: -5

2. line passing through (9, 2) and (-2, 6)

3. Graph 4x + 3y = 12.

4. Write a linear equation in slope-intercept form to model a tree 4 feet tall that grows 3 inches per year.

5. MULTIPLE CHOICE The table of ordered pairsshows the coordinates of the two points onthe graph of a function. Which equationdescribes the function?A y = -2x + 1 C y = - 1 −

2 x + 1

B y = 1 −

2 x - 1 D y = - 1 −

2 x - 1

Chapter 4 Quiz 2 (Lessons 4-3 and 4-4)

Chapter 4 Quiz 1 (Lessons 4-1 and 4-2)

x y

-2 2

4 -1

1. Write an equation in point-slope form for a line that

passes through (3, 6) with a slope of -

1 −

3 .

2. Write y - 9 = -(x + 2) in slope-intercept form.

3. Write an equation in point-slope form for a horizontal line that passes through (-4, -1).

4. Write an equation in slope-intercept form for the line that passes through (5, 3) and is parallel to x + 3y = 6.

5. MULTIPLE CHOICE Line DE contains the points D (-1, -4) and E (3, 3). Line FG contains the point F (-3, 3). Which set of coordinates for point G makes the two lines perpendicular?

A (1, 7) C (1, 4)

B (1, 10) D (4, -1)

SCORE

1.

2.

3. y

xO

4.

5.

1.

2.

3.

4.

5.


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4

4

SCORE Chapter 4 Quiz 3(Lessons 4-5 and 4-6)

1. Find the inverse of {(1, 3), (4, -1), (7, -5), (10, -9)}.

2. Graph the inverse of the functiongraphed at the right.


3. f (x) = 4x + 6 4. f (x) = 3 −

4 x - 8

5. MULTIPLE CHOICE Write the inverse of 3x + 4y = 12 in f -1 (x) notation.

A f -1 (x) = 12 - 4x −

3 B f -1 (x) = 12 - 3x −

4

C f -1 (x) = 12 - 3x D f -1 (x) = 12 - 4y

−

3

Chapter 4 Quiz 4 (Lesson 4-7)

For Questions 1–5, use the table.

Age (years) 26 27 28 29 30

Median Income

($1000)16.8 19.1 23.3 25.8 33.9

1. Make a scatter plot relating age to median income. Then draw a fit line for the scatter plot.

2. Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning.

3. Write an equation of the best-fit line for the data in the table.

4. Use the line of fit to predict the median income for 32-year olds.

5. MULTIPLE CHOICE What is the correlation coefficient for the best-fit line?

A 4.09 B –90.74 C 0.943 D 0.971

SCORE

1.

2.

3.

4.

5.

Age (years)

Med

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Inco

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($10

00)

16

19

22

25

28

31

260 27 28 29 30

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−4−8 4 8

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−4

−8


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4 SCORE

Write the letter for the correct answer in the blank at the right of each question.

1. Which is the slope-intercept form of an equation for the line containing (0, -3) with slope -1?

A y = -x - 3 B y = -3x - 1 C y = x + 3 D x = -3y - 1

2. Write an equation in slope-intercept form of the line with a slope of - 3 −

4

and y-intercept of – 5.

F y = 5x - 3 −

4 G 3x + 4y = 20 H y = -

3 −

4 x - 5 J y = -

3 −

4 x + 5

3. Write an equation of the line that passes through (-2, 8) and (-4, -4).

A y = 2x + 12 B y = 6x + 20 C y = -6x - 4 D y = 1 −

6 x + 25 −

3

4. Write y - 3 = 2 −

3 (x - 2) in standard form.

F 2x - 3y = 5 G y = 2 −

3 x + 5 −

3 H -2x + 3y = -5 J 2x - 3y = -5

5. Write y - 1 = 2 (x - 3 −

2 ) in slope-intercept form.

A 2x - y = 2 B 1 −

2 y + 1 −

2 = x C y = 2x -

1 −

2 D y = 2x - 2

6. A cell phone company charges $42 per month of service. The cost of a new cell phone, plus 8 months of service, is $415.99. How much does it cost to buy a new cell phone and 3 months of service?

F $79.99 G $126.00 H $205.99 J $289.99

Part IIFor Questions 7–10, use the following information.

Nikko needs to get his air-conditioner fixed. The technician will charge Nikko a flat fee of $50 plus an additional $20 for each hour of work.

7. Write an equation to represent Nikko’s total cost to repair his air-conditioner. Use t for total cost and h for hours.

8. Graph this equation.

9. How much will it cost Nikko if the technician has to spend 4 hours working on the air-conditioner?

10. How many hours must the technician work for it to cost Nikko $180?

1.

2.

3.

4.

5.

6.

Ass

essm

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Chapter 4 Mid-Chapter Test (Lessons 4-1 through 4-3)

Part I

7.

8.

9.

10.

1

Hours2 3 4 5 6 7 8 9 10

20406080

100

Tota

l Cos

t ($)

120140160180200


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4 SCORE

Choose from the terms above to complete each sentence.

1. If two lines have slopes that are negative reciprocals of each

other, then they are .

2. A(n) is the set of ordered pairs obtained by exchanging the x-coordinates with the y-coordinates of each ordered pair of a relation or function.

3. A graph of data points is sometimes called a

.

4. If two lines have slopes that are the same, then they are

.

5. The number that describes how closely a best-fit line models a

set of data is called the .

6. The leftmost data point in a set is (3, 27) and the rightmost point is (12, 13). If you use a linear prediction equation to findthe corresponding y-value for x = 10, you are using a method

called .

7. The leftmost data point in a set is (1997, 24) and the rightmostpoint is (2011, 38). If you use a linear prediction equation to find the corresponding y-value for x = 2012, you are using a

method called .

8. The equation y = -3x + 12 is written in form.

9. The equation y + 6 = 2(x - 4) is written in form.

Define each term in your own words.

10. line of fit

11. linear extrapolation

Chapter 4 Vocabulary Test

best-fi t line

bivariate data

correlation coefficient

inverse function

inverse relation

linear extrapolation

linear interpolation

linear regression

median-fi t line

line of fi t

parallel lines

perpendicular lines

point-slope form

rate of change

scatter plot

slope-intercept form

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.


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4 SCORE Chapter 4 Test, Form 1


For Questions 1–5, find the equation in slope-intercept form that describes each line. 1. a line with slope -2 and y-intercept 4 A y = -2x B y = 4x - 2 C y = -2x + 4 D y = 2x - 4

2. a line through (2, 4) with slope 0 F y = 2 G x = 2 H y = 4 J x = 4

3. a line through (4, 2) with slope 1 −

2

A y = - 1 −

2 x B y = 1 −

2 x - 4 C y = 2x - 10 D y = 1 −

2 x

4. a line through (-1, 1) and (2, 3) F y = 2 −

3 x + 5 −

3 G y = -

2 −

3 x + 5 −

3 H y = 2 −

3 x - 5 −

3 J y = -

2 −

3 x - 5 −

3

5. the line graphed at the right

A y = 2 −

3 x - 1 C y = 2 −

3 x + 3 −

2

B y = 3 −

2 x - 1 D y = 3 −

2 x + 3 −

2

6. If 5 deli sandwiches cost $29.75, how much will 8 sandwiches cost? F $37.75 G $29.75 H $47.60 J $0.16

7. What is the standard form of y - 8 = 2(x + 3)? A 2x + y = 14 B y = 2x + 14 C 2x - y = -14 D y - 2x = 11

8. Which is the graph of 3x - 4y = 6 ? F y

xO

G y

xO

H y

xO

J y

xO

9. Which is the point-slope form of an equation for the line that passes through (0, -5) with slope 2?

A y = 2x - 5 B y + 5 = 2x C y - 5 = x - 2 D y = 2(x + 5)

10. What is the slope-intercept form of y + 6 = 2(x + 2)? F y = 2x - 6 G y = 2x - 2 H y = 2x + 6 J 2x - y = 6

11. When are two lines parallel? A when the slopes are opposite B when the slopes are equal C when the slopes are positive D when the product of the slopes is -1

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

y

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(3, 1)

(0, -1)


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4 Chapter 4 Test, Form 1 (continued)

12. Find the slope-intercept form of an equation for the line that passes through (-1, 2) and is parallel to y = 2x - 3.

F y = 2x + 4 G y = 0.5x + 4 H y = 2x + 3 J y = -0.5x - 4

13. Find the slope-intercept form of an equation of the line perpendicular to the graph of x - 3y = 5 and passing through (0, 6).

A y = 1 −

3 x - 2 B y = -3x + 6 C y = 1 −

3 x + 2 D y = 3x - 6

For Questions 14 and 15, use the scatter plot shown.

14. How would you describe the relationship between the x- and y-values in the scatter plot?

F strong negative correlation G weak negative correlation H weak positive correlation J strong positive correlation

15. Based on the data in the scatter plot, what would you expect the y-value to be for x = 2020?

A greater than 80 C between 65 and 50 B between 80 and 65 D less than 50

16. Which equation has a slope of 2 and a y-intercept of -5? F y = -5x + 2 G y = 5x + 2 H y = 2x + 5 J y = 2x - 5

17. Which correlation coefficient corresponds to the best-fit line that most closely models its set of data?

A 0.84 B 0.13 C -0.87 D -0.15

18. The table below shows Mia’s bowling score each week she participated in a bowling league.

Week 1 2 3 4 5 6

Score 122 131 130 133 145 139

Use the median-fit line to estimate Mia’s score for week 16. F 173 G 180 H 182 J 257

19. If f(x) = 6x + 3, find f -1 (x).

A f -1 (x) = 6x - 3 B f -1 (x) = x - 6 −

3 C f -1 (x) = x - 3 −

6 D f -1 (x) = -3 - 6x

20. If f(x) = 4(3x - 5), find f -1 (x).

F f -1 (x) = x + 5 −

12 G f -1 (x) = x + 20 −

12 H f -1 (x) = x - 20 −

12 J f -1 (x) = x + 5 −

4

Bonus Find the value of r in (4, r), (r, 2) so that the slope of the

line containing them is - 5 −

3 .

0

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B:

12.

13.

14.

15.

16.

17.

18.

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4 SCORE

Ass

essm

entWrite the letter for the correct answer in the blank at the right of each question.

1. What is the slope-intercept form of the equation of a line with a slope of 5 and a y-intercept of -8?

A y = -8x + 5 B y = 8x - 5 C 5x - y = - 8 D y = 5x - 8

2. Which equation is graphed at the right? F 2y - x =10 H 2x - y = 5 G 2x + y = -5 J 2y + x = -5

3. Which is an equation of the line that passes through (2, -5) and (6, 3)?

A y = 1 −

2 x - 6 C y = 2x + 12

B y = 1 −

2 x D y = 2x - 9

4. What is an equation of the line through (0, -3) with slope 2 −

5 ?

F -5x + 2y = 15 H 2x - 5y = 15 G -5x - 2y = -15 J -2x + 5y = 15

5. Which is an equation of the line with slope -3 and a y-intercept of 5? A y = -3(x + 5) B y - 5 = -3x C -3x + y = 5 D y = 5x - 3

6. What is the equation of the line through (-2, -3) with a slope of 0?

F x = -2 G y = -3 H -2x - 3y = 0 J -3x + 2y = 0

7. Find the slope-intercept form of the equation of the line that passes through (-5, 3) and is parallel to 12x - 3y = 10.

A y = -4x - 17 B y = 4x - 13 C y = - 4x + 13 D y = 4x + 23

8. If line q has a slope of - 3 −

8 , what is the slope of any line perpendicular to q?

F -

3 −

8 G 3 −

8 H 8 −

3 J -

8 −

3

9. A line of fit might be defined as A a line that connects all the data points. B a line that might best estimate the data and be used for predicting values. C a vertical line halfway through the data. D a line that has a slope greater than 1.

10. A scatter plot of data comparing the number of years since Holbrook High School introduced a math club and the number of students participating contains the ordered pairs (3, 19) and (8, 42). Which is the slope-intercept form of an equation for the line of fit?

F y = 4.6x + 5.2 G y = 3x + 1 H y = 5.2x + 4.6 J y = 0.22x - 1.13

11. Use the equation from Question 10 to estimate the number of students who will be in the math club during the 15th year.

A 53 B 61 C 65 D 74

Chapter 4 Test, Form 2A

y

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2.

3.

4.

5.

6.

7.

8.

9.

10.

11.


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4

For Questions 12–14, use the scatter plot shown.

12. Which data are shown by the scatter plot? F (1995, 5.5), (1997, 6.1), (2004, 7.6) G (1995, 5.5), (2000, 6.1), (2004, 7.6) H (1995, 5.5), (2000, 6.6), (2005, 8.0) J (1995, 5.5), (1997, 6.6), (2005, 8.0)

13. Which is true about the data? A The slope of a best-fit line would be negative. B There is a positive correlation. C There is no correlation. D There is a negative correlation.

14. Based on the data in the scatter plot, what would you expect the y-value to be for x = 2010?

F between 7 and 8 H between 5 and 7 G higher than 8 J impossible to tell

15. To calculate the charge for a load of bricks, including delivery, the Redstone Brick Co. uses the equation C = 0.42b + 25, where C is the charge and b is the number of bricks. What is the delivery fee per load?

A $42 C $25 B $67 D It depends on the number of bricks

For Questions 16 and 17, use the table shown.

Shots on Goal 22 25 28 29 33

Points Scored 5 7 7 9 8

16. Find the slope of the best-fit line. F -0.561 G 0.283 H 0.631 J 0.794

17. Estimate how many points would be scored if 80 shots were taken on the goal using the best-fit line.

A 18 B 19 C 22 D 24

18. Find the inverse of {(4, -1), (3, -2), (6, 9), (8, 5)}. F {(8, 5), (6, 9), (3, -2), (4, -1)} H {(-1, 4), (-2, 3), (9, 6), (5, 8)} G {(-4, 1), (-3, 2), (-6, -9), (-8, -5)} J {(-1, -2), (9, 5), (4, 3), (6, 8)}

19. If f (x) = 3x - 4, find f -1 (x).

A f -1 (x) = 4x - 3 B f -1 (x) = x + 4 −

3 C f -1 (x) = x - 4 −

3 D f -1 (x) = -4 - 3x

20. If f (x) = 8(5x - 2), find f -1 (x).

F f -1 (x) = 5x + 2 −

8 G f -1 (x) = 5x - 2 −

8 H f -1 (x) = x - 16 −

40 J f -1 (x) = x + 16 −

40

Bonus What is the y-intercept of a line through (2, 7) and

perpendicular to the graph of y = -

3 −

2 x + 6?

Chapter 4 Test, Form 2A (continued)

0

5

6

7

8

'95 '00 '05 12.

13.

14.

15.

16.

17.

18.

19.

20.

B:


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4 SCORE


1. What is the slope-intercept form of the equation of the line with a slope of 1 −

4

and y-intercept at the origin? A y = 4x B y = 1 −

4 x C y = x + 1 −

4 D y + 1 −

4 = x

2. Which equation is graphed at the right? F y - 2x = -4 H 2x + y = 4 G 2x + y = -4 J y - 4 = 2x

3. Which is an equation of the line that passes through (4, -5) and (6, -9)?

A y = 1 −

2 x - 3 B y = 1 −

2 x + 3 C y = -2x + 3 D y = 2x - 3

4. What is the standard form of the equation of the line through (6, -3) with a

slope of 2 −

3 ?

F -2x + 3y = 24 G 2x - 3y = 21 H 3x - 2y = 24 J 3x - 2y = -21

5. Which is an equation of the line with a slope of -3 that passes through (2, 4)? A y - 4 = -3(x - 2) C y + 4 = -3(x + 2) B y - 4 = -3x - 2 D y - 2 = -3(x - 4)

6. What is the equation of the line through (-2, -3) with an undefined slope? F x = -2 G y = -3 H -2x - 3y = 0 J -3x + 2y = 0

7. Find the slope-intercept form of the equation of the line that passes through (-1, 5) and is parallel to 4x + 2y = 8.

A y = -2x + 9 B y = 2x - 9 C y = 4x - 9 D y = -2x + 3

8. If line q has a slope of -2, what is the slope of any line perpendicular to q? F 2 G -2 H 1 −

2 J - 1 −

2

9. The graph of data that has a strong negative correlation has A a narrow linear pattern from lower left to upper right. B a narrow linear pattern from upper left to lower right. C a narrow horizontal pattern below the x-axis. D all negative x-values.

10. A scatter plot of data comparing the time in minutes Beverly spends studying for her math test and the score she received on the test contains the ordered pairs (45, 89) and (60, 94). Which is the slope-intercept form of an equation for the line of fit?

F 0.573x + 63.2 = y G 1 −

3 x + 74 = y

H 3x - 46 = y J - 1 −

3 x + 104 = y

11. Estimate how well Beverly would score on her next test if she spent 20 minutes studying.

A 75 B 81 C 84 D 90

Chapter 4 Test, Form 2B

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y

x

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2.

3.

4.

5.

6.

7.

8.

9.

10.

11.


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4

For Questions 12–14, use the scatter plot shown.

12. Which data are shown by the scatter plot? F (1985, 47), (1995, 31), (2001, 24) G (1985, 50), (2000, 25), (2005, 0) H (47, 1985), (31, 1995), (24, 2001) J (1991, 45), (1995, 35), (2000, 8)

13. Based on the data in the scatter plot, which statement is true?

A As x increases, y increases. B As x increases, y decreases. C There is no relationship between x and y. D There are not enough data to determine the relationship between x and y.

14. Based on the scatter plot, what would you expect the y-value to be for x = 1992? F between 40 and 45 H between 30 and 40 G higher than 45 J impossible to tell

15. A baby blue whale weighed 3 tons at birth. Ten days later, it weighed 4 tons. Assuming the same rate of growth, which equation shows the weight w when the whale is d days old?

A w = 10d + 3 B w = 10d + 4 C w = 0.1d + 3 D w = d + 10

For Questions 16 and 17, use the table shown.

Times at Bat 4 5 8 12 22

Hits 1 0 2 4 6

16. Find the correlation coefficient of the best-fit line. F -0.631 G 0.317 H 0.920 J 0.959

17. Estimate how many hits a batter would get with 72 times at bat using the best-fit line.

A 18 B 19.6 C 20 D 22

18. Find the inverse of {(2, -1), (5, -2), (6, 9), (7, 5)}. F {(7, 5), (6, 9), (5, -2), (2, -1)} H {(-1, -2), (9, 5), (2, 5), (6, 7)} G {(-2, 1), (-5, 2), (-6, -9), (-7, -5)} J {(-1, 2), (-2, 5), (9, 6), (5, 7)}

19. If f (x) = 4x + 3, find f -1 (x).

A f -1 (x) = 4x - 3 B f -1 (x) = x - 3 −

4 C f -1 (x) = x - 4 −

3 D f -1 (x) = -3 - 4x

20. If f (x) = 7(2x - 9), find f -1 (x).

F f -1 (x) = x + 9 −

7 G f -1 (x) = 2x + 9 −

7 H f -1 (x) = x + 63 −

14 J f -1 (x) = x - 63 −

14

Bonus For what value of k does kx + 7y = 10 have a slope of 3?

Chapter 4 Test, Form 2B (continued)

25

30

35

40

45

'85 '95 '05

12.

13.

14.

15.

16.

17.

18.

19.

20.

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4 SCORE

1. Write a linear equation in slope-intercept form to model the situation: A telephone company charges $28.75 per month plus $0.10 a minute for long-distance calls.

2. Write an equation in standard form of the line that passes through (7, -3) and has a y-intercept of 2.

3. Write the slope-intercept form of an equation for the line graphed at the right.

4. Graph the line with a y-intercept of 3 and slope -

3 −

4 .

5. Write an equation in slope-intercept form for the line that passes through (-1, -2) and (3, 4).

6. Write an equation in standard form for the line that has an undefined slope and passes through (-6, 4).

7. Write an equation in point-slope form for the line that has slope 1 −

3 and passes through (-2, 8).

8. Write the standard form of the equation y + 4 = -

12 −

7 (x - 1).

9. Write the slope-intercept form of the equation y - 2 = 3(x - 4).

10. Write the slope-intercept form of the equation of the line parallel to the graph of 2x + y = 5 that passes through (0, 1).

11. Write the slope-intercept form of the equation of the line

perpendicular to the graph of y = -

3 −

2 x - 7 that passes

through (3, -2).

12. A scatter plot of data showing the percentage of total Internet users who visited an online store on a given day in December includes the points (2008, 2.0) and (2010, 4.5). Write the slope-intercept form of an equation for the line of fit.

1.

2.

3.

4. y

xO

5.

6.

7.

8.

9.

10.

11.

12.

Chapter 4 Test, Form 2C

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4

For Questions 13–15, use the data in the table.

Time Spent Studying (min) 10 20 30 40 50

Score Received (percent) 53 67 78 87 95

13. Make a scatter plot relating time spent studying to the score received.

14. Write the slope-intercept form of the equation for a line of fit for the data. Use your equation to predict a student’s score if the student spent 35 minutes studying.

15. Is it reasonable to use the equation to estimate the score received for any length of time spent studying?

For Questions 16 and 17, use the data in the table showing the number of congressional seats apportioned to California each decade.

Decade 1940s 1950s 1970s 1990s 2000s

Seats 23 30 43 52 53

Source: Office of the Clerk, U.S. House of Representatives

16. Find an equation for the median-fit line.

17. Predict the number of seats apportioned to California in the 1930s.

18. Graph the inverse of the function graphed at the right.

19. If f (x) = 5 - 4x −

15 , find f -1 (x).

20. Write the inverse of 6x + 8y = 13 in f -1 (x) notation.

Bonus In a certain lake, a 1-year-old bluegill fish is 3 inches long, while a 4-year-old bluegill fish is 6.6 inches long. Assuming the growth rate can be approximated by a linear equation, write an equation in slope-intercept form for the length � of a bluegill fish in inches after t years. Then use the equation to determine the age of a 9-inch bluegill.

Chapter 4 Test, Form 2C (continued)

13.

14.

15.

16.

17.

18. y

xO

8

4

−4−8 4 8

−4

−8

19.

20.

B:

Time Spent Studying(minutes)

Sco

re R

ecei

ved

(per

cen

t)

0

60

70

80

90

100

10 20 30 40 50

y

xO

8

4

−4−8 4 8

−4

−8


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4 SCORE

1. Write a linear equation in slope-intercept form to model the situation: An Internet company charges $4.95 per month plus $2.50 for each hour of use.

2. Write an equation in standard form of the line that passes through (3, 1) and has a y-intercept of -2.

3. Write the slope-intercept form of an equation for the line graphed at the right.

4. Graph the line with y-intercept 2 and slope -

1 −

2 .

5. Write an equation in slope-intercept form for the line that passes through (5, 4) and (6, -1).

6. Write an equation in standard form for the line that has an undefined slope and passes through (5, -3).

7. Write an equation in point-slope form for the line that has

a slope of 4 −

3 and passes through (3, 0).

8. Write the standard form of the equation y - 3 = - 2 −

3 (x + 5).

9. Write the slope-intercept form of the equation

y - 1 = 3 −

4 (x - 3).

10. Write the slope-intercept form of the equation of the line parallel to the graph of 9x + 3y = 6 that passes through (5, 3).

11. Write the slope-intercept form of the equation of the line perpendicular to the graph of 4x - y = 12 that passes through (8, 2).

12. A scatter plot of data showing the percentage of total Internet users who visit a video sharing Web site on a given day in December includes the points (2010, 17.0) and (2008, 0.3). Write the slope-intercept form of an equation for the line of fit.

Chapter 4 Test, Form 2D

y

xO

1.

2.

3.

4. y

xO

5.

6.

7.

8.

9.

10.

11.

12.


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4

For Questions 13–15, use the data that shows age and percent of budget spent on entertainment in the table.

Age 30 40 50 60 70 80

Percent Spent on Entertainment 6.1 6.0 5.4 5.0 4.7 3.4

13. Make a scatter plot relating the age to the percent of the person’s budget spent on entertainment.

14. Write the slope-intercept form of the equation for a line of fit for the data. Use your equation to predict the percent of a 65-year-old person’s budget.

15. Is it reasonable to use the equation to estimate the entertainment spending for any age?

For Questions 16 and 17, use the data in the table showing the number of congressional seats apportioned to Texas each decade.

Decade 1960s 1970s 1980s 1990s 2000s

Seats 23 24 27 30 32


16. Find an equation for the median-fit line.

17. Predict the number of seats that will be apportioned to Texas in the 2010s.

18. Graph the inverse of the graph shown.

19. If f (x) = 8 - 3x −

18 , find f -1 (x).

20. Write the inverse of 5x - 17 = 11 + 3y in f -1 (x) notation.

Bonus Write an equation in slope-intercept form of the line with y-intercept -6 and parallel to a line perpendicular to 5x + 6y - 13 = 0.

Chapter 4 Test, Form 2D (continued)

13.

14.

15.

16.

17.

18. y

xO

8

4

−4−8 4 8

−4

−8

19.

20.

B:

Age

Perc

ent

Spen

t o

nEn

tert

ain

men

t

3

4

5

6

300 40 50 60 70 80

y

xO

8

4

−4−8 4 8

−4

−8


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4 SCORE

For Questions 1–4, write an equation in slope-intercept form of the line satisfying the given conditions.

1. has y-intercept -8 and slope 3

2. has slope 5 −

2 and passes through (4, -1)

3. passes through (-3, 7) and (2, 4)

4. is horizontal and passes through (-4, 6)

5. Write the point-slope form of an equation of the line that has a slope of - 3 −

5 and passes through (2, 1).

6. Write an equation in standard form of the line that passes through (2, -3) and (-3, 7).

7. Graph a line that has an x-intercept of 5 and a slope of - 3 −

5 .

8. Write y + 4 = - 2 −

3 (x - 9) in standard form.

9. Write the point-slope form of the equation for the line that has x-intercept -3 and y-intercept -2.

For Questions 10–13, write an equation in slope-intercept form of the line satisfying the given conditions.

10. is parallel to the y-axis and has an x-intercept of 3

11. is perpendicular to 4y = 3x - 8 and passes through (-12, 7)

12. is parallel to 3x - 5y = 7 and passes through (0, -6)

13. is perpendicular to the y-axis and passes through (-2, 5)

Chapter 4 Test, Form 3

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

y

xO


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4

For Questions 14–16, use the data in the table.

14. Make a scatter plot relating the verbal scores and the math scores.

State Graduation Scores

Year Verbal Score Math Score

1975 460 488

1985 424 466

1995 410 463

2005 420 460

15. Does the scatter plot in Question 14 show a positive, a negative, or no correlation? What does that relationship represent?

16. Write the equation for a line of fit. Predict the corresponding math score for a verbal score of 445.

17. The data in the table show the number of congressional seats apportioned to the state of New York each decade.

Decade 1940s 1960s 1980s 2000s

Seats 45 41 34 29


Find an equation for the median-fit line and predict the number of seats that will be apportioned to New York in the 2020s.

18. Graph the inverse of the function graphed at the right.

19. If f (x) = 3(4 - 5x) −

8 , find f -1 (x).

20. Write the inverse of 4x - 13 = 2x + 3y in f -1 (x) notation.

Bonus The area of a circle varies directly as the square of the radius. If the radius is tripled, by what factor will the area increase?

Chapter 4 Test, Form 3 (continued)

14.

15.

16.

17.

18. y

xO

8

4

−4−8 4 8

−4

−8

19.

20.

B:

Verbal Score

Mat

h S

core

450

460

470

480

490

500

4000 440 480

y

xO

8

4

−4−8 4 8

−4

−8


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4 SCORE

Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solution in more than one way or investigate beyond the requirements of the problem.

1. You are told that a line passes through (-2, 3). a. Discuss what other information you would need to graph this

line. b. Then describe how you would use that information to graph

the line and write its equation.

2. Refer to the scatter plot at the right. a. Describe the pattern of points in the

scatter plot and the relationship between x and y.

b. Give at least two examples of real-life situations that, if graphed, would result in a correlation like the one shown in this scatter plot.

c. Add a scale and heading to each axis. Then write an equation that would model the points represented by this plot.

3. The table gives the life expectancy of a child born in the United States in a given year.

a. Make a scatter plot of the data. b. Can you use the data to claim

that the increase in life expectancy is due to improved health care? Explain your response.

c. Use the data to predict the life expectancy of a baby born in 2000. Explain how you determined your answer.

Source: National Center for Health Statistics

Chapter 4 Extended-Response Test

y

xO

Years of Life Expected at Birth

Year of Birth

Life Expectancy (years)

1920 54.1

1930 59.7

1940 62.9

1950 68.2

1960 69.7

1970 70.8

1980 73.7

1985 74.7

1990 75.4

1995 75.8


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4 SCORE Standardized Test Practice(Chapters 1–4)

1. If a = 2, b = 6, and c = 4, then (4a - b) 2 −

(b + c) = ? (Lesson 1-2)

A 4 B 0.4 C 40 D 0.04 1. A B C D

2. If 4 + 7 + 6 = 4 + 7 + 6 + n, what is the value of n? (Lesson 1-3)

F 0 G 1 H 4 J 6 2. F G H J

3. Lynn has 4 more books than José. If Lynn gives José 6 of her books, how many more will José have than Lynn? (Lesson 1-2)

A 2 B 4 C 8 D 10 3. A B C D

4. If x = 16 −

24 , which value of x does not form a proportion? (Lesson 2-6)

F 2 −

3 G 3 −

4 H 12 −

18 J 32 −

48 4. F G H J

5. Two-thirds of a number added to itself is 20. What is the number?

(Lesson 2-1)

A 12 B 13 C 30 D 33 5. A B C D

6. 16% of 980 is 9.8% of what number? (Lesson 2-4)

F 1.6 G 16 H 160 J 1600 6. F G H J

7. For what value(s) of r is 3r - 6 = 7 + 3r? (Lesson 2-7)

A all numbers C 0 B all negative integers D no values of r 7. A B C D

8. The range of a relation includes the integers x −

4 , x −

5 , and x −

8 .

What could be a value for x in the domain? (Lesson 1-6)

F 20 G 30 H 32 J 40 8. F G H J

9. A line with a slope of -1 passes through points at (2, 3) and (5, y). Find the value of y. (Lesson 3-3)

A -6 B -3 C 0 D 6 9. A B C D

10. If a line passes through (0, -6) and has a slope of -3, what is an equation for the line? (Lesson 4-2)

F y = -6x - 3 H y = -3x - 6 G x = -6y - 3 J x = -3y - 6 10. F G H J

Part 1: Multiple Choice

Instructions: Fill in the appropriate circle for the best answer.


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4 Standardized Test Practice (continued)

11. If f (x) = 21 - 6x −

5 , find f -1 (x).

A f -1 (x) = 5x - 21 −

6 C f -1 (x) = 21 + 5x −

6

B f -1 (x) = 21 - 5x −

6 D f -1 (x) = 21 - 6x −

5 11. A B C D

12. If x + 2x + 3x −

2 = 6, x = ? (Lesson 2-3)

F 1 −

2 G 1 H 2 J 4 12. F G H J

13. Find the slope of the line that passes through (2, 2) and (7, 7). (Lesson 3-3)

A -1 B 1 C -5 D 5 13. A B C D

14. What is an equation of the line that passes through (1, 2) and (0, –1)? (Lesson 4-2)

F y = x – 3 G y = – x + 3 H y = – 3x + 1 J y = 3x – 1 14. F G H J

15. The formula for the volume of a rectangular solid is V = Bh. A packing crate has a height of 4.5 inches and a base area of 18.2 square inches. What is the volume of the crate in cubic inches? (Lesson 2-8)

16. Find the slope of a line parallel to the

graph of 1 −

2 y = x + 6. (Lesson 4-4)

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

. . . . .

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

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9

8

7

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2

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9

8

7

6

5

4

3

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9

8

7

6

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4

3

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9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

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Part 2: Gridded Response

Instructions: Enter your answers by writing each digit of the answer in a column box

and then shading in the appropriate circle that corresponds to that entry.


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4 Standardized Test Practice (continued)

17. Write 2 � r � r � t � t using exponents. (Lesson 1-1)

18. Evaluate 2xy - y2 if x = 6 and y = 12. (Lesson 1-2)

Simplify each expression. (Lessons 1-2 through 1-5)

19. 12 - 6 × 5 20. 6(2 + 3) - 9

21. (2 � 3)2 - 22 22. 4 � 9 - 2 � 10

23. 4(2y + y) - 6(4y + 3y) 24. 12a - 18b −

-6

For Questions 25–27, solve each equation. (Lessons 2-2 and 2-3)

25. 13 - m = 21

26. 3 −

4 x = 2 −

3

27. 4x + 12 = -16

28. Solve x - 2y = 12 if the domain is {-3, -1, 0, 2, 5}.(Lesson 3-1)

29. Determine whether {(1, 4), (2, 6), (3, 7), (4, 4)} is a function, and explain your reasoning. (Lesson 1-7)

30. Write an equation for the relationship between the variables in the chart. (Lesson 3-6)

x 0 2 4 6

y 2 5 8 11

31. Determine the slope of the line passing through (2, 7) and (-5, 2). (Lesson 4-3)

32. Write an equation in slope-intercept form for the line passing through (2, 6) with a slope of -3. (Lesson 4-1)

33. Write an equation for the line passing through (-6, 5) and (-6, -4). (Lesson 4-2)

34. Lucy owns a bakery. In 2006, she sold pies for $9.50 each. In 2010, she sold pies for $17.50 each. (Lesson 3-3)

a. Find the rate of change for the price of a pie from 2006 to 2010.

b. How much do you think Lucy will sell a pie for in 2014?

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34a.

34b.

Part 3: Short Response

Instructions: Write your answers in the space.


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Chapter 4 A1 Glencoe Algebra 1

Chapter Resources

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

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Lesson 4-1

4-1

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pe

an

d b

is t

he

y-in

terc

ep

t

W

rite

an

eq

uat

ion

in

slo

pe-

inte

rcep

t fo

rm f

or t

he

lin

e w

ith

a s

lop

e of

-4

and

a y

-in

terc

ept

of 3

.

y =

mx

+ b

S

lope-inte

rcept

form

y =

-4x

+ 3

R

epla

ce m

with -

4 a

nd b

with 3

.

G

rap

h 3

x -

4y

= 8

.

3x -

4y

= 8

O

rigin

al equation

-

4y =

-3x

+ 8

S

ubtr

act

3x

from

each s

ide.

-

4y

−

-4

= -

3x +

8

−

-4

D

ivid

e e

ach s

ide b

y -

4.

y

= 3 −

4 x -

2

Sim

plif

y.

Th

e y-

inte

rcep

t of

y =

3 −

4 x -

2 i

s -

2 an

d th

e sl

ope

is 3 −

4 . S

o gr

aph

th

e po

int

(0, -

2). F

rom

th

is p

oin

t, m

ove

up

3 u

nit

s an

d ri

ght

4 u

nit

s. D

raw

a l

ine

pass

ing

thro

ugh

bot

h p

oin

ts.

Exer

cise

sW

rite

an

eq

uat

ion

of

a li

ne

in s

lop

e-in

terc

ept

form

wit

h t

he

give

n s

lop

e an

d

y-in

terc

ept.

1. s

lope

: 8, y

-in

terc

ept

-3

2. s

lope

: -2,

y-i

nte

rcep

t -

1 3.

slo

pe: -

1, y

-in

terc

ept

-7

y

= 8

x -

3

y =

-2x

- 1

y

= -

x -

7

Wri

te a

n e

qu

atio

n i

n s

lop

e-in

terc

ept

form

for

eac

h g

rap

h s

how

n.

4.

( 0, –

2)

( 1, 0

)x

y

O

5.

( 3, 0

)

( 0, 3

)

x

y

O

6.

( 4, –

2)

( 0, –

5)

xy

O

y

= 2

x -

2

y =

-x +

3

y =

3 −

4 x -

5

Gra

ph

eac

h e

qu

atio

n.

7. y

= 2

x +

1

8. y

= -

3x +

2

9. y

= -

x -

1

x

y

O

x

y

O

x

y

O

( 0, –

2)

( 4, 1

)

x

y

O

3x -

4y

= 8

Exam

ple

1

Exam

ple

2

001_

012_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

512

/21/

10

12:4

5 A

M

A01-A12_ALG1_A_CRM_C04_AN_660499.indd A1A01-A12_ALG1_A_CRM_C04_AN_660499.indd A1 12/21/10 1:23 AM12/21/10 1:23 AM

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

4-1

Cha

pte

r 4

6 G

lenc

oe A

lgeb

ra 1

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Gra

ph

ing

Eq

uati

on

s i

n S

lop

e-I

nte

rcep

t Fo

rm

Mo

del

ing

Rea

l-W

orl

d D

ata

MED

IA S

ince

199

9, t

he

nu

mb

er o

f m

usi

c ca

sset

tes

sold

has

d

ecre

ased

by

an a

vera

ge r

ate

of 2

7 m

illi

on p

er y

ear.

Th

ere

wer

e 12

4 m

illi

on m

usi

c ca

sset

tes

sold

in

199

9.

a.

Wri

te a

lin

ear

equ

atio

n t

o fi

nd

th

e av

erag

e n

um

ber

of

mu

sic

cass

ette

s so

ld i

n

any

year

aft

er 1

999.

T

he

rate

of

chan

ge i

s -

27 m

illi

on p

er y

ear.

In t

he

firs

t ye

ar, t

he

nu

mbe

r of

mu

sic

cass

ette

s so

ld w

as 1

24 m

illi

on. L

et N

= t

he

nu

mbe

r of

mil

lion

s of

mu

sic

cass

ette

s so

ld.

Let

x =

th

e n

um

ber

of y

ears

sin

ce 1

999.

An

equ

atio

n i

s N

= -

27x

+ 1

24.

b.

Gra

ph

th

e eq

uat

ion

.

Th

e gr

aph

of

N =

-27

x +

124

is

a li

ne

that

pas

ses

thro

ugh

th

e po

int

at (

0, 1

24)

and

has

a s

lope

of

-27

.

c.

Fin

d t

he

app

roxi

mat

e n

um

ber

of

mu

sic

cass

ette

s so

ld i

n 2

003.

N

= -

27x

+ 1

24

Ori

gin

al equation

N

= -

27(4

) +

124

R

epla

ce x

with 4

.

N

= 1

6 S

implif

y.

T

her

e w

ere

abou

t 16

mil

lion

mu

sic

cass

ette

s so

ld i

n 2

003.

Exer

cise

s 1

. MU

SIC

In

200

1, f

ull

-len

gth

cas

sett

es r

epre

sen

ted

3.4%

of

tota

l m

usi

c sa

les.

Bet

wee

n 2

001

and

2006

, th

e pe

rcen

t de

crea

sed

by a

bou

t 0.

5% p

er y

ear.

a. W

rite

an

equ

atio

n t

o fi

nd

the

perc

ent

P o

f re

cord

ed m

usi

c so

ld a

s fu

ll-l

engt

h c

asse

ttes

for

an

y ye

ar x

bet

wee

n

2001

an

d 20

06.

b.

Gra

ph t

he

equ

atio

n o

n t

he

grid

at

the

righ

t.c.

Fin

d th

e pe

rcen

t of

rec

orde

d m

usi

c so

ld

as f

ull

-len

gth

cas

sett

es i

n 2

004.

2. P

OPU

LATI

ON

Th

e po

pula

tion

of

the

Un

ited

Sta

tes

is

proj

ecte

d to

be

300

mil

lion

by

the

year

201

0. B

etw

een

20

10 a

nd

2050

, th

e po

pula

tion

is

expe

cted

to

incr

ease

by

abo

ut

2.5

mil

lion

per

yea

r.a.

Wri

te a

n e

quat

ion

to

fin

d th

e po

pula

tion

P i

n a

ny

year

x

betw

een

201

0 an

d 20

50.

b.

Gra

ph t

he

equ

atio

n o

n t

he

grid

at

the

righ

t.

c. F

ind

the

popu

lati

on i

n 2

050.

ab

ou

t 40

0,0

00,

00

0

Full-

leng

th C

asse

tte

Sale

s

Percent of Total Music Sales

1.5%

2.0%

1.0%

2.5%

3.0%

3.5%

Year

s Si

nce

2001

32

10

54

Proj

ecte

d Un

ited

Stat

es P

opul

atio

n

Year

s Si

nce

2010

Population (millions)

020

40x

P

400

380

360

340

320

300

Mus

ic C

asse

ttes

Sol

d

Cassettes (millions)

5075 25

0

100

125

Year

s Si

nce

1999

32

15

74

6

Exam

ple

P =

-0.

5x +

3.4 1.9%

P =

2,5

00,

00

0x +

30

0,0

00,

00

0

001_

012_

ALG

1_A

_CR

M_C

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9.in

dd

612

/21/

10

12:4

5 A

M

Lesson X-1


NA

ME

DAT

E

P

ER

IOD

Lesson 4-1

4-1

Cha

pte

r 4

7 G

lenc

oe A

lgeb

ra 1

Skill

s Pr

acti

ceG

rap

hin

g E

qu

ati

on

s i

n S

lop

e-I

nte

rcep

t Fo

rmW

rite

an

eq

uat

ion

of

a li

ne

in s

lop

e-in

terc

ept

form

wit

h t

he

give

n s

lop

e an

d y

-in

terc

ept.

1. s

lope

: 5, y

-in

terc

ept:

-3

y =

5x -

3

2. s

lope

: -2,

y-i

nte

rcep

t: 7

y =

-2x

+ 7

3. s

lope

: -6,

y-i

nte

rcep

t: -

2 y =

-6x

- 2

4.

slo

pe: 7

, y-i

nte

rcep

t: 1

y =

7x +

1

5. s

lope

: 3, y

-in

terc

ept:

2 y

= 3

x +

2

6. s

lope

: -4,

y-i

nte

rcep

t: -

9 y =

-4x

- 9

7. s

lope

: 1, y

-in

terc

ept:

-12

y =

x -

12

8. s

lope

: 0, y

-in

terc

ept:

8 y

= 8

Wri

te a

n e

qu

atio

n i

n s

lop

e-in

terc

ept

form

for

eac

h g

rap

h s

how

n.

9.

( 2, 1

)

( 0, –

3)

x

y

O

10

.

( 0, 2

)

( 2, –

4)

x

y

O

11

.

( 0, –

1)( 2

, –3)

x

y O

y

= 2

x -

3

y =

-3x

+ 2

y

= -

x -

1

Gra

ph

eac

h e

qu

atio

n.

12. y

= x

+ 4

13

. y =

-2x

- 1

14

. x +

y =

-3

x

y

O

x

y

O

x

y

O

15. V

IDEO

REN

TALS

A v

ideo

sto

re c

har

ges

$10

for

a re

nta

l ca

rd

plu

s $2

per

ren

tal.

a. W

rite

an

equ

atio

n i

n s

lope

-in

terc

ept

form

for

th

e to

tal

cost

c o

f bu

yin

g a

ren

tal

card

an

d re

nti

ng

m

mov

ies.

b.

Gra

ph t

he

equ

atio

n.

c. F

ind

the

cost

of

buyi

ng

a re

nta

l ca

rd a

nd

ren

tin

g 6

mov

ies.

$2

2

Vide

o St

ore

Rent

al C

osts

Total Cost ($)

10 01214161820c

Mov

ies

Rent

ed1

23

45

m

c =

10

+ 2m

c =

10

+ 2

m

001_

012_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

712

/21/

10

12:4

5 A

M

Answers (Lesson 4-1)


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

4-1

Cha

pte

r 4

8 G

lenc

oe A

lgeb

ra 1

Prac

tice

Gra

ph

ing

Eq

uati

on

s i

n S

lop

e-I

nte

rcep

t Fo

rmW

rite

an

eq

uat

ion

of

a li

ne

in s

lop

e-in

terc

ept

form

wit

h t

he

give

n s

lop

e an

d

y-in

terc

ept.

1. s

lope

: 1 −

4 , y-

inte

rcep

t: 3

y =

1 −

4 x +

3

2. s

lope

: 3 −

2 , y-

inte

rcep

t: -

4 y =

3 −

2 x -

4

3. s

lope

: 1.5

, y-i

nte

rcep

t: -

1 4.

slo

pe: -

2.5,

y-i

nte

rcep

t: 3

.5

y

= 1

.5x -

1

y =

-2.

5x +

3.5

Wri

te a

n e

qu

atio

n i

n s

lop

e-in

terc

ept

form

for

eac

h g

rap

h s

how

n.

5.

( –5,

0)

( 0, 2

)

x

y

O

6.

( –2,

0)

( 0, 3

)

x

y O

7.

( –3,

0)

( 0, –

2)

x

y

O

y =

2 −

5 x +

2

y =

3 −

2 x +

3

y =

-

2 −

3 x -

2

Gra

ph

eac

h e

qu

atio

n.

8. y

= -

1 −

2 x +

2

9. 3

y =

2x

- 6

10

. 6x

+ 3

y =

6

x

y

O

x

y

O

x

y

O

11. W

RIT

ING

Car

la h

as a

lrea

dy w

ritt

en 1

0 pa

ges

of a

nov

el.

Sh

e pl

ans

to w

rite

15

addi

tion

al p

ages

per

mon

th u

nti

l sh

e is

fin

ish

ed.

a. W

rite

an

equ

atio

n t

o fi

nd

the

tota

l n

um

ber

of p

ages

P

wri

tten

aft

er a

ny

nu

mbe

r of

mon

ths

m.

P =

10

+ 1

5m

b.

Gra

ph t

he

equ

atio

n o

n t

he

grid

at

the

righ

t.

c. F

ind

the

tota

l n

um

ber

of p

ages

wri

tten

aft

er 5

mon

ths.

85

Carl

a’s

Nov

el

Mon

ths

Pages Written

20

46

13

5m

P

100 80 60 40 20

001_

012_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

812

/21/

10

12:4

5 A

M


NA

ME

DAT

E

P

ER

IOD

Lesson 4-1

4-1

Cha

pte

r 4

9 G

lenc

oe A

lgeb

ra 1

Wor

d Pr

oble

m P

ract

ice

Gra

ph

ing

Eq

uati

on

s i

n S

lop

e-I

nte

rcep

t Fo

rm

1.SA

VIN

GS

Wad

e’s

gran

dmot

her

gav

e h

im

$100

for

his

bir

thda

y. W

ade

wan

ts t

o sa

ve h

is m

oney

to

buy

a n

ew M

P3

play

er

that

cos

ts $

275.

Eac

h m

onth

, he

adds

$2

5 to

his

MP

3 sa

vin

gs. W

rite

an

eq

uat

ion

in

slo

pe-i

nte

rcep

t fo

rm f

or x

, th

e n

um

ber

of m

onth

s th

at i

t w

ill

take

Wad

e to

sav

e $2

75.

2

75 =

25x

+ 1

00

2. C

AR

CA

RE

Su

ppos

e re

gula

r ga

soli

ne

cost

s $2

.76

per

gall

on. Y

ou c

an p

urc

has

e a

car

was

h a

t th

e ga

s st

atio

n f

or $

3. T

he

grap

h o

f th

e eq

uat

ion

for

th

e co

st o

f x

gall

ons

of g

asol

ine

and

a ca

r w

ash

is

show

n b

elow

. Wri

te t

he

equ

atio

n i

n s

lope

-in

terc

ept

form

for

th

e li

ne.

Gas

olin

e (g

al)

32

10

54

98

710

y

x6

Cost of gas and car wash ($)

68 4 21016 14 121824 22 20

( 4, 1

4.04

)

( 2, 8

.52)

( 0, 3

)

y=

2.7

6x+

3

3. A

DU

LT E

DU

CA

TIO

N A

ngi

e’s

mot

her

w

ants

to

take

som

e ad

ult

edu

cati

on

clas

ses

at t

he

loca

l h

igh

sch

ool.

Sh

e h

as

to p

ay a

on

e-ti

me

enro

llm

ent

fee

of $

25

to jo

in t

he

adu

lt e

duca

tion

com

mu

nit

y,

and

then

$45

for

eac

h c

lass

sh

e w

ants

to

take

. Th

e eq

uat

ion

y =

45x

+ 2

5 ex

pres

ses

the

cost

of

taki

ng

x cl

asse

s.

Wh

at a

re t

he

slop

e an

d y-

inte

rcep

t of

th

e eq

uat

ion

?

m

= 4

5; y

-in

terc

ept

= 2

5

4.B

USI

NES

S A

con

stru

ctio

n c

rew

nee

ds t

o re

nt

a tr

ench

dig

ger

for

up

to a

wee

k. A

n

equ

ipm

ent

ren

tal

com

pan

y ch

arge

s $4

0 pe

r da

y pl

us

a $2

0 n

on-r

efu

nda

ble

insu

ran

ce c

ost

to r

ent

a tr

ench

dig

ger.

Wri

te a

nd

grap

h a

n e

quat

ion

to

fin

d th

e to

tal

cost

to

ren

t th

e tr

ench

dig

ger

for

d d

ays.

Day

s3

21

05

49

87

6

Price ($)

100

140 60 20180

300

340

260

220

5. E

NER

GY

Fro

m 2

002

to 2

005,

U.S

. co

nsu

mpt

ion

of

ren

ewab

le e

ner

gy

incr

ease

d an

ave

rage

of

0.17

qu

adri

llio

n

BT

Us

per

year

. Abo

ut

6.07

qu

adri

llio

n

BT

Us

of r

enew

able

pow

er w

ere

prod

uce

d in

th

e ye

ar 2

002.

a. W

rite

an

equ

atio

n i

n s

lope

-in

terc

ept

form

to

fin

d th

e am

oun

t of

ren

ewab

le

pow

er P

(qu

adri

llio

n B

TU

s) p

rodu

ced

in y

ear

y be

twee

n 2

002

and

2005

. P

= 0

.17y

+ 6

.07

b.

App

roxi

mat

ely

how

mu

ch r

enew

able

po

wer

was

pro

duce

d in

200

5?6.

58 q

uad

rilli

on

BT

Us

c. I

f th

e sa

me

tren

d co

nti

nu

es f

rom

200

6 to

201

0, h

ow m

uch

ren

ewab

le p

ower

w

ill

be p

rodu

ced

in t

he

year

201

0?

7.43

qu

adri

llio

n B

TU

s

y =

40d

+ 2

0

001_

012_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

912

/21/

10

12:4

5 A

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass


Lesson X-2


NA

ME

DAT

E

P

ER

IOD

Lesson 4-2

4-2

Cha

pte

r 4

11

Gle

ncoe

Alg

ebra

1

Exer

cise

sW

rite

an

eq

uat

ion

of

the

lin

e th

at p

asse

s th

rou

gh t

he

give

n p

oin

t an

d h

as t

he

give

n s

lop

e.

1.

( 3, 5

)

x

y

O

m =

2

2.

( 0, 0

)x

y

O

m =

–2

3.

( 2, 4

)

x

y

O

m =

1 2

y

= 2

x -

1

y =

-2x

y

= 1 −

2 x +

3

4. (

8, 2

); sl

ope

-

3 −

4 5.

(-

1, -

3); s

lope

5

6. (

4, -

5); s

lope

-

1 −

2

y

= -

3 −

4 x +

8

y =

5x +

2

y =

-

1 −

2 x -

3

7. (

-5,

4);

slop

e 0

8. (

2, 2

); sl

ope

1 −

2 9.

(1,

-4)

; slo

pe -

6

y

= 4

y

= 1 −

2 x +

1

y =

-6x

+ 2

10. (

-3,

0),

m =

2

11. (

0, 4

), m

= -

3 12

. (0,

350

), m

= 1

−

5

y

= 2

x +

6

y =

-3x

+ 4

y

= 1 −

5 x +

350

Stud

y G

uide

and

Inte

rven

tion

Wri

tin

g E

qu

ati

on

s i

n S

lop

e-I

nte

rcep

t Fo

rm

Wri

te a

n E

qu

atio

n G

iven

th

e Sl

op

e an

d a

Po

int

W

rite

an

eq

uat

ion

of

the

lin

e th

at p

asse

s th

rou

gh (

-4,

2)

wit

h a

slo

pe

of 3

.T

he

lin

e h

as s

lope

3. T

o fi

nd

the

y-in

terc

ept,

rep

lace

m w

ith

3 a

nd

(x, y

) w

ith

(-

4, 2

) in

th

e sl

ope-

inte

rcep

t fo

rm.

Th

en s

olve

for

b.

y =

mx

+ b

S

lope-inte

rcept

form

2 =

3(-

4) +

b

m =

3,

y =

2,

and x

= -

4

2 =

-12

+ b

M

ultip

ly.

14 =

b

Add 1

2 t

o e

ach s

ide.

Th

eref

ore,

th

e eq

uat

ion

is

y =

3x

+ 1

4.

W

rite

an

eq

uat

ion

of

the

lin

eth

at p

asse

s th

rou

gh (

-2,

-1)

wit

h a

sl

ope

of 1 −

4 .T

he

lin

e h

as s

lope

1 −

4 . R

epla

ce m

wit

h 1 −

4 an

d (x

, y)

wit

h (

-2,

-1)

in

th

e sl

ope-

inte

rcep

t fo

rm.

y

= m

x +

b

Slo

pe-inte

rcept

form

-1

= 1 −

4 (-

2) +

b

m =

1 −

4 , y =

-1,

and x

= -

2

-1

= -

1 −

2 + b

M

ultip

ly.

- 1 −

2 = b

A

dd 1

−

2 to

each s

ide.

Th

eref

ore,

th

e eq

uat

ion

is

y =

1 −

4 x -

1 −

2 .

Exam

ple

1Ex

amp

le 2

001_

012_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

1112

/21/

10

12:4

5 A

M


NA

ME

DAT

E

P

ER

IOD

4-1

Cha

pte

r 4

10

Gle

ncoe

Alg

ebra

1

Enri

chm

ent

Usin

g E

qu

ati

on

s: Id

eal W

eig

ht

You

can

fin

d yo

ur

idea

l w

eigh

t as

fol

low

s.A

wom

an s

hou

ld w

eigh

100

pou

nds

for

th

e fi

rst

5 fe

et o

f h

eigh

t an

d 5

addi

tion

al p

oun

ds f

or e

ach

in

ch o

ver

5 fe

et (

5 fe

et =

60

inch

es).

A m

an s

hou

ld w

eigh

106

pou

nds

for

th

e fi

rst

5 fe

et o

f h

eigh

t an

d 6

addi

tion

al p

oun

ds f

or e

ach

in

ch o

ver

5 fe

et. T

hes

e fo

rmu

las

appl

y to

pe

ople

wit

h n

orm

al b

one

stru

ctu

res.

To

dete

rmin

e yo

ur

bon

e st

ruct

ure

, wra

p yo

ur

thu

mb

and

inde

x fi

nge

r ar

oun

d th

e w

rist

of

you

r ot

her

han

d. I

f th

e th

um

b an

d fi

nge

r ju

st t

ouch

, yo

u h

ave

nor

mal

bon

e st

ruct

ure

. If

they

ove

rlap

, you

are

sm

all-

bon

ed.

If t

hey

don

’t ov

erla

p, y

ou a

re l

arge

-bon

ed. S

mal

l-bo

ned

peo

ple

shou

ld d

ecre

ase

thei

r ca

lcu

late

d id

eal

wei

ght

by 1

0%. L

arge

-bon

ed p

eopl

e sh

ould

in

crea

se t

he

valu

e by

10%

.

Cal

cula

te t

he

idea

l w

eigh

ts o

f th

ese

peo

ple

.1.

wom

an, 5

ft

4 in

., n

orm

al-b

oned

2.

man

, 5 f

t 11

in

., la

rge-

bon

ed

120

lb

189

.2 lb

3. m

an, 6

ft

5 in

., sm

all-

bon

ed

4. y

ou, i

f yo

u a

re a

t le

ast

5 ft

tal

l

187

.2 lb

A

nsw

ers

will

var

y.

For

Exe

rcis

es 5

–9, u

se t

he

foll

owin

g in

form

atio

n.

Su

ppos

e a

nor

mal

-bon

ed m

an i

s x

inch

es t

all.

If h

e is

at

leas

t 5

feet

ta

ll, t

hen

x -

60

repr

esen

ts t

he

nu

mbe

r of

in

ches

th

is m

an i

s ov

er

5 fe

et t

all.

For

eac

h o

f th

ese

inch

es, h

is i

deal

wei

ght

is i

ncr

ease

d by

6

pou

nds

. Th

us,

his

pro

per

wei

ght

y is

giv

en b

y th

e fo

rmu

la

y =

6(x

- 6

0) +

106

or

y =

6x

- 2

54. I

f th

e m

an i

s la

rge-

bon

ed, t

he

form

ula

bec

omes

y =

6x

- 2

54 +

0.1

0(6x

- 2

54).

5. W

rite

th

e fo

rmu

la f

or t

he

wei

ght

of a

lar

ge-b

oned

man

in

slo

pe-i

nte

rcep

t fo

rm.

6. D

eriv

e th

e fo

rmu

la f

or t

he

idea

l w

eigh

t y

of a

nor

mal

-bon

ed

fem

ale

wit

h h

eigh

t x

inch

es. W

rite

th

e fo

rmu

la i

n

slop

e-in

terc

ept

form

.

7. D

eriv

e th

e fo

rmu

la i

n s

lope

-in

terc

ept

form

for

th

e id

eal

wei

ght

y of

a l

arge

-bon

ed f

emal

e w

ith

hei

ght

x in

ches

.

8. D

eriv

e th

e fo

rmu

la i

n s

lope

-in

terc

ept

form

for

th

e id

eal

wei

ght

y of

a s

mal

l-bo

ned

mal

e w

ith

hei

ght

x in

ches

.

9. F

ind

the

hei

ghts

at

wh

ich

th

e id

eal

wei

ghts

of

nor

mal

-bon

ed m

ales

and

larg

e-bo

ned

fem

ales

wou

ld b

e th

e sa

me.

y =

6.6

x -

279

.4

y =

5x -

20

0

y =

5.5

x -

220

y =

5.4

x -

228

.6

68 in

., o

r 5

ft 8

in.

001_

012_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

1012

/21/

10

12:4

5 A

M

Answers (Lesson 4-1 and Lesson 4-2)


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

4-2

Cha

pte

r 4

12

Gle

ncoe

Alg

ebra

1

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Wri

tin

g E

qu

ati

on

s i

n S

lop

e-I

nte

rcep

t Fo

rm

Wri

te a

n E

qu

atio

n G

iven

Tw

o P

oin

ts

W

rite

an

eq

uat

ion

of

the

lin

e th

at p

asse

s th

rou

gh (

1, 2

) an

d (

3, -

2).

Fin

d th

e sl

ope

m. T

o fi

nd

the

y-in

terc

ept,

rep

lace

m w

ith

its

com

pute

d va

lue

and

(x, y

) w

ith

(1

, 2)

in t

he

slop

e-in

terc

ept

form

. Th

en s

olve

for

b.

m =

y 2 -

y 1

−

x 2 -

x 1

Slo

pe form

ula

m =

-2

- 2

−

3 -

1

y 2 =

-2,

y 1 =

2,

x 2 =

3,

x 1 =

1

m =

-2

Sim

plif

y.

y =

mx

+ b

S

lope-inte

rcept

form

2 =

-2(

1) +

b

Repla

ce m

with -

2,

y w

ith 2

, and x

with 1

.

2 =

-2

+ b

M

ultip

ly.

4 =

b

Add 2

to e

ach s

ide.

Th

eref

ore,

th

e eq

uat

ion

is

y =

-2x

+ 4

.

Exer

cise

sW

rite

an

eq

uat

ion

of

the

lin

e th

at p

asse

s th

rou

gh e

ach

pai

r of

poi

nts

.

1.

( 1, 1

)

( 0, –

3)

x

y

O

2.

( 0

, 4) ( 4

, 0)

x

y

O

3.

( 0, 1

)

( –3,

0)

x

y

O

y

= 4

x -

3

y =

-x +

4

y =

1 −

3 x +

1

4. (

-1,

6),

(7, -

10)

5. (

0, 2

), (1

, 7)

6. (

6, -

25),

(-1,

3)

y

= -

2x +

4

y =

5x +

2

y =

-4x

- 1

7. (

-2,

-1)

, (2,

11)

8.

(10

, -1)

, (4,

2)

9. (

-14

, -2)

, (7,

7)

y

= 3

x +

5

y =

-

1 −

2 x +

4

y =

3 −

7 x +

4

10. (

4, 0

), (0

, 2)

11. (

-3,

0),

(0, 5

) 12

. (0,

16)

, (-

10, 0

)

y

= -

1 −

2 x +

2

y =

5 −

3 x +

5

y =

8 −

5 x +

16

Exam

ple

001_

012_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

1212

/21/

10

12:4

5 A

M


NA

ME

DAT

E

P

ER

IOD

Lesson 4-2

Cha

pte

r 4

13

Gle

ncoe

Alg

ebra

1

Wri

te a

n e

qu

atio

n o

f th

e li

ne

that

pas

ses

thro

ugh

th

e gi

ven

poi

nt

wit

h t

he

give

n s

lop

e.

1.

( –1,

4)

x

y

O

m =

–3

2.

( 4

, 1)

x

y

O

m =

1

3.

( -1,

2)

x

y O

m =

2

y

= -

3x +

1

y =

x -

3

y =

2x +

4

4. (

1, 9

); sl

ope

4 5.

(4,

2);

slop

e -

2 6.

(2,

-2)

; slo

pe 3

y

= 4

x +

5

y =

-2x

+ 1

0 y

= 3

x -

8

7. (

3, 0

); sl

ope

5 8.

(-

3, -

2); s

lope

2

9. (

-5,

4);

slop

e -

4

y =

5x -

15

y =

2x +

4

y =

-4x

- 1

6

Wri

te a

n e

qu

atio

n o

f th

e li

ne

that

pas

ses

thro

ugh

eac

h p

air

of p

oin

ts.

10.

( –2,

3)

( 3, –

2)

x

y

O

11

.

( –1,

–3)

( 1, 1

)x

y

O

12

.

( 2, –

1)

( 0, 3

)

x

y

O

y

= -

x +

1

y =

2x -

1

y =

-2x

+ 3

13. (

1, 3

), (-

3, -

5)

14. (

1, 4

), (6

, -1)

15

. (1,

-1)

, (3,

5)

y

= 2

x +

1

y =

-x +

5

y =

3x -

4

16. (

-2,

4),

(0, 6

) 17

. (3,

3),

(1, -

3)

18. (

-1,

6),

(3, -

2)

y =

x +

6

y =

3x -

6

y =

-2x

+ 4

19. I

NV

ESTI

NG

Th

e pr

ice

of a

sh

are

of s

tock

in

XY

Z C

orpo

rati

on w

as $

74 t

wo

wee

ks a

go.

Sev

en w

eeks

ago

, th

e pr

ice

was

$59

a s

har

e.

a. W

rite

a l

inea

r eq

uat

ion

to

fin

d th

e pr

ice

p of

a s

har

e of

XY

Z C

orpo

rati

on s

tock

w w

eeks

fro

m n

ow.

p =

3w

+ 8

0

b.

Est

imat

e th

e pr

ice

of a

sh

are

of s

tock

fiv

e w

eeks

ago

.$ 6

5

Skill

s Pr

acti

ceW

riti

ng

Eq

uati

on

s i

n S

lop

e-I

nte

rcep

t Fo

rm

4-2

013_

023_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

1312

/21/

10

12:4

6 A

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

14

Gle

ncoe

Alg

ebra

1

Prac

tice

Wri

tin

g E

qu

ati

on

s i

n S

lop

e-I

nte

rcep

t Fo

rm

Wri

te a

n e

qu

atio

n o

f th

e li

ne

that

pas

ses

thro

ugh

th

e gi

ven

poi

nt

and

has

th

e gi

ven

slo

pe.

1.

( 1, 2

)

x

y

O

m =

3

2.

( –2,

2)

x

y O

m =

–2

3.

( –1,

–3)

x

y

O

m =

–1

y

= 3

x -

1

y =

-2x

- 2

y

= -

x -

4

4. (

-5,

4);

slop

e -

3 5.

(4,

3);

slop

e 1 −

2 6.

(1,

-5)

; slo

pe -

3 −

2

y

= -

3x -

11

y =

1 −

2 x +

1

y =

-

3 −

2 x -

7 −

2

7. (

3, 7

); sl

ope

2 −

7 8.

(-

2, 5 −

2 ) ; s

lope

-

1 −

2 9.

(5, 0

); sl

ope

0

y

= 2 −

7 x +

6 1 −

7 y

= -

1 −

2 x +

3 −

2 y

= 0

Wri

te a

n e

qu

atio

n o

f th

e li

ne

that

pas

ses

thro

ugh

eac

h p

air

of p

oin

ts.

10.

( 4, –

2)

( 2, –

4)

x

y

O

11

. ( 0

, 5)

( 4, 1

) x

y

O

12

. ( –

3, 1

)

( –1,

–3)

x

y

O

y

= x

- 6

y

= -

x +

5

y =

-2x

- 5

13. (

0, -

4), (

5, -

4)

14. (

-4,

-2)

, (4,

0)

15. (

-2,

-3)

, (4,

5)

y

= -

4 y

= 1 −

4 x -

1

y =

4 −

3 x -

1 −

3

16. (

0, 1

), (5

, 3)

17. (

-3,

0),

(1, -

6)

18. (

1, 0

), (5

, -1)

y

= 2 −

5 x +

1

y =

-

3 −

2 x -

9 −

2

y =

-

1 −

4 x +

1 −

4

19. D

AN

CE

LESS

ON

S T

he

cost

for

7 d

ance

les

son

s is

$82

. Th

e co

st f

or 1

1 le

sson

s is

$12

2.

Wri

te a

lin

ear

equ

atio

n t

o fi

nd

the

tota

l co

st C

for

ℓ l

esso

ns.

Th

en u

se t

he

equ

atio

n t

o fi

nd

the

cost

of

4 le

sson

s.

20. W

EATH

ER I

t is

76°

F a

t th

e 60

00-f

oot

leve

l of

a m

oun

tain

, an

d 49

°F a

t th

e 12

,000

-foo

t le

vel

of t

he

mou

nta

in. W

rite

a l

inea

r eq

uat

ion

to

fin

d th

e te

mpe

ratu

re T

at

an e

leva

tion

x

on t

he

mou

nta

in, w

her

e x

is i

n t

hou

san

ds o

f fe

et.

C =

10ℓ

+ 1

2; $

52

T =

-4.

5x +

103

4-2

013_

023_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

1412

/21/

10

12:4

6 A

M

Lesson X-2


NA

ME

DAT

E

P

ER

IOD

Lesson 4-2

Cha

pte

r 4

15

Gle

ncoe

Alg

ebra

1

Wor

d Pr

oble

m P

ract

ice

Wri

tin

g E

qu

ati

on

s i

n S

lop

e-I

nte

rcep

t Fo

rm

1.FU

ND

RA

ISIN

G Y

von

ne

and

her

fri

ends

h

eld

a ba

ke s

ale

to b

enef

it a

sh

elte

r fo

r h

omel

ess

peop

le. T

he

frie

nds

sol

d 22

cak

es o

n t

he

firs

t da

y an

d 15

cak

es o

n

the

seco

nd

day

of t

he

bake

sal

e. T

hey

co

llec

ted

$88

on t

he

firs

t da

y an

d $6

0 on

th

e se

con

d da

y. L

et x

rep

rese

nt

the

nu

mbe

r of

cak

es s

old

and

y re

pres

ent

the

amou

nt

of m

oney

mad

e. F

ind

the

slop

e of

th

e li

ne

that

wou

ld p

ass

thro

ugh

th

e po

ints

giv

en.

4

2. J

OB

S M

r. K

imba

ll r

ecei

ves

a $3

000

ann

ual

sal

ary

incr

ease

on

th

e an

niv

ersa

ry o

f h

is h

irin

g if

he

rece

ives

a

sati

sfac

tory

per

form

ance

rev

iew

. H

is s

tart

ing

sala

ry w

as $

41,2

50. W

rite

an

equ

atio

n t

o sh

ow k

, Mr.

Kim

ball

’s

sala

ry a

fter

t y

ears

at

this

com

pan

y if

his

per

form

ance

rev

iew

s ar

e al

way

s sa

tisf

acto

ry.

k

= 3

00

0t +

41,

250

3.C

ENSU

S T

he

popu

lati

on o

f L

ared

o,

Tex

as, w

as a

bou

t 21

5,50

0 in

200

7. I

t w

as

abou

t 12

3,00

0 in

199

0. I

f w

e as

sum

e th

at t

he

popu

lati

on g

row

th i

s co

nst

ant

and

t re

pres

ents

th

e n

um

ber

of y

ears

af

ter

1990

, wri

te a

lin

ear

equ

atio

n t

o fi

nd

p, L

ared

o’s

popu

lati

on f

or a

ny

year

af

ter

1990

.

p =

544

1t +

123

,00

0

4.W

ATE

R M

r. W

illi

ams

pays

$40

a m

onth

fo

r ci

ty w

ater

, no

mat

ter

how

man

y ga

llon

s of

wat

er h

e u

ses

in a

giv

en

mon

th. L

et x

rep

rese

nt

the

nu

mbe

r of

ga

llon

s of

wat

er u

sed

per

mon

th. L

et y

repr

esen

t th

e m

onth

ly c

ost

of t

he

city

w

ater

in

dol

lars

. Wh

at i

s th

e eq

uat

ion

of

the

lin

e th

at r

epre

sen

ts t

his

in

form

atio

n?

Wh

at i

s th

e sl

ope

of t

he

lin

e?

y

= 4

0; s

lop

e is

0. T

he

line

is

ho

rizo

nta

l.

5. S

HO

E SI

ZES

Th

e ta

ble

show

s h

ow

wom

en’s

sh

oe s

izes

in

th

e U

nit

ed

Kin

gdom

com

pare

to

wom

en’s

sh

oe s

izes

in

th

e U

nit

ed S

tate

s.

Wo

men

’s S

ho

e S

izes

U.K

.3

3.5

44

.55

5.5

6

U.S

.5

.56

6.5

77.

58

8.5

Sour

ce: D

ance

Spor

t U

K

a. W

rite

a l

inea

r eq

uat

ion

to

dete

rmin

e an

y U

.S. s

ize

y if

you

are

giv

en t

he

U.K

. siz

e x.

y =

x +

2.5

b.

Wh

at a

re t

he

slop

e an

d y-

inte

rcep

t of

th

e li

ne?

slo

pe

= 1

; y

-inte

rcep

t =

2.5

c. I

s th

e y-

inte

rcep

t a

vali

d da

ta p

oin

t fo

r th

e gi

ven

in

form

atio

n?

No

. It

is n

ot

likel

y a

valid

dat

a p

oin

t b

ecau

se t

he

U.K

. siz

ing

p

rob

ably

do

es n

ot

incl

ud

e ze

ro. H

ow

ever

, th

e p

oin

t is

th

e y-i

nte

rcep

t o

f th

e lin

e re

pre

sen

ted

by

the

dat

a if

th

e d

ata

wer

e to

co

nti

nu

e in

defi

nit

ely

in b

oth

dir

ecti

on

s.

4-2

013_

023_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

1512

/21/

10

12:4

6 A

M



Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

16

Gle

ncoe

Alg

ebra

1

Tan

gen

t to

a C

urv

eA

tan

gen

t li

ne

is a

lin

e th

at i

nte

rsec

ts a

cu

rve

at a

poi

nt

wit

h t

he

sam

e ra

te o

f ch

ange

, or

slop

e, a

s th

e ra

te o

f ch

ange

of

the

curv

e at

th

at p

oin

t.

For

qu

adra

tic

fun

ctio

ns,

fu

nct

ion

s of

th

e fo

rm y

= a

x2 +

bx

+

c,

equ

atio

ns

of t

he

tan

gen

t li

nes

ca

n b

e fo

un

d. T

his

is

base

d on

th

e fa

ct t

hat

th

e sl

ope

thro

ugh

an

y tw

o po

ints

on

th

e cu

rve

is e

qual

to

the

slop

e of

th

e li

ne

tan

gen

t to

th

e cu

rve

at t

he

poin

t w

hos

e x-

valu

e is

hal

fway

be

twee

n t

he

x-va

lues

of

the

oth

er t

wo

poin

ts.

F

ind

an

eq

uat

ion

of

the

lin

e ta

nge

nt

to t

he

curv

e y

= x

2 +

3x

+ 2

th

rou

gh t

he

poi

nt

(2, 1

2).

Fir

st f

ind

two

poin

ts o

n t

he

curv

e w

hos

e x-

valu

es a

re

equ

idis

tan

t fr

om t

he

x-va

lue

of (

2, 1

2).

Ste

p 1

: F

ind

two

poin

ts o

n t

he

curv

e. U

se x

= 1

an

d x

= 3

.

Wh

en x

=

1, y

=

12

+ 3(

1) +

2 o

r 6.

W

hen

x =

3, y

=

32

+ 3

(3)

+ 2

or

20.

S

o, t

he

two

orde

red

pair

s ar

e (1

, 6)

and

(3, 2

0).

Ste

p 2

: F

ind

the

slop

e of

th

e li

ne

that

pas

ses

thro

ugh

th

ese

two

poin

ts.

m

= 20

- 6

−

3 -

1

or 7

Ste

p 3

: N

ow u

se t

his

slo

pe a

nd

the

poin

t (2

, 12)

to

fin

d an

equ

atio

n o

f th

e ta

nge

nt

lin

e.

y =

mx

+ b

S

lope-inte

rcept

form

12

= 7

(2)

+ b

R

epla

ce x

with 2

, y

with 1

2,

and m

with 7

.

-

2 =

b

S

olv

e for

b.

So,

an

equ

atio

n o

f th

e ta

nge

nt

lin

e to

y =

x2

+ 3x

+

2

thro

ugh

th

e po

int

(2, 1

2) i

s y

= 7x

– 2

.

Exer

cise

sF

ind

an

eq

uat

ion

of

the

lin

e ta

nge

nt

to e

ach

cu

rve

thro

ugh

th

e gi

ven

poi

nt.

1. y

= x

2 - 3

x +

7,

(2,

5)

2. y

= 3

x2 + 4

x -

5, (

-4,

27)

3.

y =

5 -

x2 ,

(1, 4

)

y =

x +

3

y =

-20

x -

53

y =

-2x

+ 6

4. F

ind

the

slop

e of

th

e li

ne

tan

gen

t to

th

e cu

rve

at x

= 0

for

th

e ge

ner

al e

quat

ion

y

= a

x2 + b

x +

c.

m

= b

5. F

ind

the

slop

e of

th

e li

ne

tan

gen

t to

th

e cu

rve

y =

ax2 +

bx

+ c

at

x by

fin

din

g th

e sl

ope

of t

he

lin

e th

rou

gh t

he

poin

ts (

0, c

) an

d (2

x, 4

ax2 +

2bx

+ c

). D

oes

this

equ

atio

n f

ind

the

sam

e sl

ope

for

x =

0 a

s yo

u f

oun

d in

Exe

rcis

e 4?

m

= 2

ax +

b, y

es

Enri

chm

ent

y

xO

Exam

ple

4-2

013_

023_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

1612

/21/

10

12:4

6 A

M


NA

ME

DAT

E

P

ER

IOD

Lesson 4-3

Cha

pte

r 4

17

Gle

ncoe

Alg

ebra

1

Stud

y G

uide

and

Inte

rven

tion

Wri

tin

g E

qu

ati

on

s i

n P

oin

t-S

lop

e F

orm

Poin

t-Sl

op

e Fo

rm

Po

int-

Slo

pe

Form

y -

y1 =

m(x

- x

1),

wh

ere

(x 1

, y 1

) is

a g

ive

n p

oin

t o

n a

no

nve

rtic

al lin

e

an

d m

is t

he

slo

pe

of

the

lin

e

W

rite

an

eq

uat

ion

in

p

oin

t-sl

ope

form

for

th

e li

ne

that

pas

ses

thro

ugh

(6,

1)

wit

h a

slo

pe

of -

5 −

2 .

y -

y1

= m

(x -

x1)

P

oin

t-slo

pe form

y -

1 =

-

5 −

2 (x -

6)

m =

- 5

−

2 ;

(x1,

y 1)

= (

6,

1)

Th

eref

ore,

th

e eq

uat

ion

is

y -

1 =

-

5 −

2 (x -

6).

W

rite

an

eq

uat

ion

in

p

oin

t-sl

ope

form

for

a h

oriz

onta

l li

ne

that

pas

ses

thro

ugh

(4,

-1)

.

y

- y

1 =

m(x

- x

1)

Poin

t-slo

pe form

y -

(-

1) =

0(x

- 4

) m

= 0

; (x

1,

y 1)

= (

4,

-1)

y

+ 1

= 0

S

implif

y.

Th

eref

ore,

th

e eq

uat

ion

is

y +

1 =

0.

Exer

cise

sW

rite

an

eq

uat

ion

in

poi

nt-

slop

e fo

rm f

or t

he

lin

e th

at p

asse

s th

rou

gh e

ach

poi

nt

wit

h t

he

give

n s

lop

e.

1.

( 4, 1

)

x

y

O

m =

1

2.

( –3,

2)

x

y

O

m =

0

3.

( 2, –

3)

x

y

O

m =

–2

y

- 1

= x

- 4

y

- 2

= 0

y

+ 3

= -

2(x -

2)

4. (

2, 1

), m

= 4

5.

(-7,

2),

m =

6

6. (8

, 3),

m =

1

y -

1 =

4(x

- 2

) y

- 2

= 6

(x +

7)

y -

3 =

x -

8

7. (

-6,

7),

m =

0

8. (4

, 9),

m =

3 −

4 9.

(-4,

-5)

, m =

-

1 −

2

y

- 7

= 0

y

- 9

= 3 −

4 (x -

4)

y +

5 =

-

1 −

2 (x +

4)

10. W

rite

an

equ

atio

n i

n p

oin

t-sl

ope

form

for

a h

oriz

onta

l li

ne

that

pas

ses

thro

ugh

(4

, -2)

.

11. W

rite

an

equ

atio

n i

n p

oin

t-sl

ope

form

for

a h

oriz

onta

l li

ne

that

pas

ses

thro

ugh

(-

5, 6

).

12. W

rite

an

equ

atio

n i

n p

oin

t-sl

ope

form

for

a h

oriz

onta

l li

ne

that

pas

ses

thro

ugh

(5,

0).

y

= 0

Exam

ple

1Ex

amp

le 2

y +

2 =

0

y -

6 =

0

4-3

013_

023_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

1712

/21/

10

12:4

6 A

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

18

Gle

ncoe

Alg

ebra

1

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Wri

tin

g E

qu

ati

on

s i

n P

oin

t-S

lop

e F

orm

Form

s o

f Li

nea

r Eq

uat

ion

sS

lop

e-In

terc

ept

Form

y =

mx

+ b

m =

slo

pe

; b

= y

-in

terc

ep

t

Po

int-

Slo

pe

Form

y -

y1 =

m(x

- x

1)

m =

slo

pe

; (x

1,

y 1)

is a

giv

en

po

int

Sta

nd

ard

Form

Ax

+ B

y =

CA

an

d B

are

no

t b

oth

ze

ro. U

su

ally

A is n

on

ne

ga

tive

an

d A

, B

, a

nd

C a

re in

teg

ers

wh

ose

gre

ate

st

co

mm

on

fa

cto

r is

1.

W

rite

y +

5 =

2 −

3 (x -

6)

in

stan

dar

d f

orm

.

y

+ 5

= 2 −

3 (x -

6)

Ori

gin

al equation

3(

y +

5)

= 3

( 2 −

3 ) (x

- 6

) M

ultip

ly e

ach s

ide b

y 3

.

3y

+ 1

5 =

2(x

- 6

) D

istr

ibutive

Pro

pert

y

3y

+ 1

5 =

2x

- 1

2 D

istr

ibutive

Pro

pert

y

3y

= 2

x -

27

Subtr

act

15 f

rom

each s

ide.

-2x

+ 3

y =

-27

A

dd -

2x

to e

ach s

ide.

2x

- 3

y =

27

Multip

ly e

ach s

ide b

y -

1.

Th

eref

ore,

th

e st

anda

rd f

orm

of

the

equ

atio

n

is 2

x -

3y

= 2

7.

W

rite

y -

2 =

- 1 −

4 (x -

8)

in

slop

e-in

terc

ept

form

.

y -

2 =

-

1 −

4 (x -

8)

Ori

gin

al equation

y -

2 =

-

1 −

4 x +

2

Dis

trib

utive

Pro

pert

y

y

= -

1 −

4 x +

4

Add 2

to e

ach s

ide.

Th

eref

ore,

th

e sl

ope-

inte

rcep

t fo

rm o

f th

e eq

uat

ion

is

y =

-

1 −

4 x +

4.

Exer

cise

sW

rite

eac

h e

qu

atio

n i

n s

tan

dar

d f

orm

.

1. y

+ 2

= -

3(x

- 1

) 2.

y -

1 =

-

1 −

3 (x -

6)

3. y

+ 2

= 2 −

3 (x -

9)

3

x +

y =

1

x +

3y =

9

2x -

3y =

24

4. y

+ 3

= -

(x -

5)

5. y

- 4

= 5 −

3 (x +

3)

6. y

+ 4

= -

2 −

5 (x -

1)

x

+ y

= 2

5

x -

3y =

-27

2

x +

5y =

-18

Wri

te e

ach

eq

uat

ion

in

slo

pe-

inte

rcep

t fo

rm.

7. y

+ 4

= 4

(x -

2)

8. y

- 5

= 1

−

3 (x -

6)

9. y

- 8

= -

1 −

4 (x +

8)

y

= 4

x -

12

y =

1 −

3 x +

3

y =

-

1 −

4 x +

6

10. y

- 6

= 3

(x -

1 −

3 ) 11

. y +

4 =

-2(

x +

5)

12. y

+ 5 −

3 = 1 −

2 (x -

2)

y

= 3

x +

5

y =

-2x

- 1

4 y

= 1 −

2 x -

8 −

3

Exam

ple

1Ex

amp

le 2

4-3

013_

023_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

1812

/21/

10

12:4

6 A

M


NA

ME

DAT

E

P

ER

IOD

Lesson 4-3

Cha

pte

r 4

19

Gle

ncoe

Alg

ebra

1

Skill

s Pr

acti

ceW

riti

ng

Eq

uati

on

s i

n P

oin

t-S

lop

e F

orm

Wri

te a

n e

qu

atio

n i

n p

oin

t-sl

ope

form

for

th

e li

ne

that

pas

ses

thro

ugh

eac

h p

oin

t w

ith

th

e gi

ven

slo

pe.

1.

( –1,

–2)

x

y

O

m =

3

2.

( 1, –

2)x

y O

m =

–1

3.

( 2, –

3)

x

y O

m =

0

y

+ 2

= 3

(x +

1)

y +

2 =

-(x

- 1

) y

+ 3

= 0

4. (

3, 1

), m

= 0

5.

(-

4, 6

), m

= 8

6.

(1,

-3)

, m =

-4

y

- 1

= 0

y

- 6

= 8

(x +

4)

y +

3 =

-4(

x -

1)

7. (

4, -

6), m

= 1

8.

(3,

3),

m =

4 −

3 9.

(-

5, -

1), m

= -

5 −

4

y

+ 6

= x

- 4

y

- 3

= 4 −

3 (x -

3)

y +

1 =

-

5 −

4 (x +

5)

Wri

te e

ach

eq

uat

ion

in

sta

nd

ard

for

m.

10. y

+ 1

= x

+ 2

11

. y +

9 =

-3(

x -

2)

12. y

- 7

= 4

(x +

4)

x

- y

= -

1 3

x +

y =

-3

4x -

y =

-23

13. y

- 4

= -

(x -

1)

14. y

- 6

= 4

(x +

3)

15. y

+ 5

= -

5(x

- 3

)

x

+ y

= 5

4

x -

y =

-18

5

x +

y =

10

16. y

- 1

0 =

-2(

x -

3)

17. y

- 2

= -

1 −

2 (x -

4)

18. y

+ 1

1 =

1 −

3 (x +

3)

2

x +

y =

16

x +

2y =

8

x -

3y =

30

Wri

te e

ach

eq

uat

ion

in

slo

pe-

inte

rcep

t fo

rm.

19. y

- 4

= 3

(x -

2)

20. y

+ 2

= -

(x +

4)

21. y

- 6

= -

2(x

+ 2

)

y

= 3

x -

2

y =

-x -

6

y =

-2x

+ 2

22. y

+ 1

= -

5(x

- 3

) 23

. y -

3 =

6(x

- 1

) 24

. y -

8 =

3(x

+ 5

)

y

= -

5x +

14

y =

6x -

3

y =

3x +

23

25. y

- 2

= 1 −

2 (x +

6)

26. y

+ 1

= -

1 −

3 (x +

9)

27. y

- 1 −

2 = x

+ 1 −

2

y

= 1 −

2 x +

5

y =

-

1 −

3 x -

4

y =

x +

1

4-3

013_

023_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

1912

/21/

10

12:4

6 A

M



Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

20

Gle

ncoe

Alg

ebra

1

Prac

tice

Wri

tin

g E

qu

ati

on

s i

n P

oin

t-S

lop

e F

orm

Wri

te a

n e

qu

atio

n i

n p

oin

t-sl

ope

form

for

th

e li

ne

that

pas

ses

thro

ugh

eac

h p

oin

t w

ith

th

e gi

ven

slo

pe.

1. (

2, 2

), m

= -

3 2.

(1,

-6)

, m =

-1

3. (

-3,

-4)

, m =

0

y

- 2

= -

3(x -

2)

y +

6 =

-(x

- 1

) y

+ 4

= 0

4. (

1, 3

), m

= -

3 −

4 5.

(-

8, 5

), m

= -

2 −

5 6.

(3,

-3)

, m =

1 −

3

y

- 3

= -

3 −

4 (x -

1)

y -

5 =

-

2 −

5 (x +

8)

y +

3 =

1 −

3 (x -

3)

Wri

te e

ach

eq

uat

ion

in

sta

nd

ard

for

m.

7. y

- 1

1 =

3(x

- 2

) 8.

y -

10

= -

(x -

2)

9. y

+ 7

= 2

(x +

5)

3

x -

y =

-5

x +

y =

12

2x -

y =

-3

10. y

- 5

= 3 −

2 (x +

4)

11. y

+ 2

= -

3 −

4 (x +

1)

12. y

- 6

= 4 −

3 (x -

3)

3

x -

2y =

-22

3

x +

4y =

-11

4

x -

3y =

-6

13. y

+ 4

= 1

.5(x

+ 2

) 14

. y -

3 =

-2.

4(x

- 5

) 15

. y -

4 =

2.5

(x +

3)

3

x -

2y =

2

12x

+ 5

y =

75

5x -

2y =

-23

Wri

te e

ach

eq

uat

ion

in

slo

pe-

inte

rcep

t fo

rm.

16. y

+ 2

= 4

(x +

2)

17. y

+ 1

= -

7(x

+ 1

) 18

. y -

3 =

-5(

x +

12)

y

= 4

x +

6

y =

-7x

- 8

y

= -

5x -

57

19. y

- 5

= 3 −

2 (x +

4)

20. y

- 1 −

4 = -

3 (

x +

1 −

4 ) 21

. y -

2 −

3 = -

2 (x

- 1 −

4 )

y

= 3 −

2 x +

11

y =

-3x

- 1 −

2 y

= -

2x +

7 −

6

22. C

ON

STR

UC

TIO

N A

con

stru

ctio

n c

ompa

ny

char

ges

$15

per

hou

r fo

r de

bris

rem

oval

, pl

us

a on

e-ti

me

fee

for

the

use

of

a tr

ash

du

mps

ter.

Th

e to

tal

fee

for

9 h

ours

of

serv

ice

is $

195.

a. W

rite

th

e po

int-

slop

e fo

rm o

f an

equ

atio

n t

o fi

nd

the

tota

l fe

e y

for

any

nu

mbe

r of

h

ours

x.

b.

Wri

te t

he

equ

atio

n i

n s

lope

-in

terc

ept

form

. y =

15x

+ 6

0

c. W

hat

is

the

fee

for

the

use

of

a tr

ash

du

mps

ter?

$60

23. M

OV

ING

Th

ere

is a

dai

ly f

ee f

or r

enti

ng

a m

ovin

g tr

uck

, plu

s a

char

ge o

f $0

.50

per

mil

e dr

iven

. It

cost

s $6

4 to

ren

t th

e tr

uck

on

a d

ay w

hen

it

is d

rive

n 4

8 m

iles

.

a. W

rite

th

e po

int-

slop

e fo

rm o

f an

equ

atio

n t

o fi

nd

the

tota

l ch

arge

y f

or a

on

e-da

y re

nta

l w

ith

x m

iles

dri

ven

.

b.

Wri

te t

he

equ

atio

n i

n s

lope

-in

terc

ept

form

.

c. W

hat

is

the

dail

y fe

e? $

40

y -

195

= 1

5(x -

9)

y -

64

= 0

.5(x

- 4

8)

y =

0.5

x +

40

4-3

013_

023_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

2012

/21/

10

12:4

6 A

M


NA

ME

DAT

E

P

ER

IOD

Lesson 4-3

Cha

pte

r 4

21

Gle

ncoe

Alg

ebra

1

1.B

ICY

CLI

NG

Har

vey

ride

s h

is b

ike

at a

n

aver

age

spee

d of

12

mil

es p

er h

our.

In

oth

er w

ords

, he

ride

s 12

mil

es i

n 1

hou

r, 24

mil

es i

n 2

hou

rs, a

nd

so o

n. L

et h

be

the

nu

mbe

r of

hou

rs h

e ri

des

and

d b

e di

stan

ce t

rave

led.

Wri

te a

n e

quat

ion

for

th

e re

lati

onsh

ip b

etw

een

dis

tan

ce a

nd

tim

e in

poi

nt-

slop

e fo

rm.

d

- 1

2 =

12(

h -

1)

2. G

EOM

ETRY

Th

e pe

rim

eter

of

a sq

uar

e va

ries

dir

ectl

y w

ith

its

sid

e le

ngt

h. T

he

poin

t-sl

ope

form

of

the

equ

atio

n f

or t

his

fu

nct

ion

is

y -

4 =

4(x

- 1

). W

rite

th

e eq

uat

ion

in

sta

nda

rd f

orm

.

4

x -

y =

0

3.N

ATU

RE

Th

e fr

equ

ency

of

a m

ale

cric

ket’s

ch

irp

is r

elat

ed t

o th

e ou

tdoo

r te

mpe

ratu

re. T

he

rela

tion

ship

is

expr

esse

d by

th

e eq

uat

ion

T =

n +

40,

w

her

e T

is

the

tem

pera

ture

in

deg

rees

Fa

hre

nh

eit

and

n i

s th

e n

um

ber

of c

hir

ps

the

cric

ket

mak

es i

n 1

4 se

con

ds. U

se

the

info

rmat

ion

fro

m t

he

grap

h b

elow

to

wri

te a

n e

quat

ion

for

th

e li

ne

in p

oin

t-sl

ope

form

.

N

um

ber

of

Ch

irp

s15

105

025

20

y

x30

35

Temperature (°F)

3040 20 105070 60

S

amp

le a

nsw

er:

T -

60

= 1

(n -

20)

4.C

AN

OEI

NG

Geo

ff p

addl

es h

is c

anoe

at

an a

vera

ge s

peed

of

3.5

mil

es p

er h

our.

Aft

er 5

hou

rs o

f ca

noe

ing,

Geo

ff h

as

trav

eled

18

mil

es. W

rite

an

equ

atio

n i

n

poin

t-sl

ope

form

to

fin

d th

e to

tal

dist

ance

y

for

any

nu

mbe

r of

hou

rs x

.

y -

18

= 3

.5(x

- 5

)

5. A

VIA

TIO

N A

jet

plan

e ta

kes

off

and

con

sist

entl

y cl

imbs

20

feet

for

eve

ry

40 f

eet

it m

oves

hor

izon

tall

y. T

he

grap

h

show

s th

e tr

ajec

tory

of

the

jet.

Ho

rizo

nta

l Dis

tan

ce (

ft)

500

010

0015

0020

0025

00

Height (ft)

600

800

400

200

1000

1400

1200

a. W

rite

an

equ

atio

n i

n p

oin

t-sl

ope

form

fo

r th

e li

ne

repr

esen

tin

g th

e je

t’s

traj

ecto

ry.

y -

0 =

0.5

(x -

0)

b.

Wri

te t

he

equ

atio

n f

rom

par

t a

in

slop

e -i

nte

rcep

t fo

rm.

c. W

rite

th

e eq

uat

ion

in

sta

nda

rd f

orm

. x

- 2

y =

0

Wor

d Pr

oble

m P

ract

ice

Wri

tin

g E

qu

ati

on

s i

n P

oin

t-S

lop

e F

orm

y =

0.5

x

4-3

013_

023_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

2112

/21/

10

12:4

6 A

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

22

Gle

ncoe

Alg

ebra

1

Enri

chm

ent

x

y O

x

y

O

Co

llin

eari

ty

You

hav

e le

arn

ed h

ow t

o fi

nd

the

slop

e be

twee

n t

wo

poin

ts o

n a

lin

e. D

oes

it m

atte

r w

hic

h t

wo

poin

ts y

ou u

se?

How

doe

s yo

ur

choi

ce o

f po

ints

aff

ect

the

slop

e-in

terc

ept

form

of

the

equ

atio

n o

f th

e li

ne?

1. C

hoo

se t

hre

e di

ffer

ent

pair

s of

poi

nts

fro

m t

he

grap

h a

t th

e

righ

t. W

rite

th

e sl

ope-

inte

rcep

t fo

rm o

f th

e li

ne

usi

ng

each

pai

r.

y

= x

+ 1

2. H

ow a

re t

he

equ

atio

ns

rela

ted?

T

hey

are

th

e sa

me.

3. W

hat

con

clu

sion

can

you

dra

w f

rom

you

r an

swer

s to

Exe

rcis

es 1

an

d 2?

T

he

equ

atio

n o

f a

line

is t

he

sam

e n

o m

atte

r w

hic

h t

wo

po

ints

yo

u c

ho

ose

.

Wh

en p

oin

ts a

re c

onta

ined

in

th

e sa

me

lin

e, t

hey

are

sai

d to

be

coll

inea

r.

Eve

n th

ough

poi

nts

may

loo

k li

ke t

hey

form

a l

ine

whe

n co

nnec

ted,

it

does

not

mea

n t

hat

th

ey a

ctu

ally

do.

By

chec

kin

g pa

irs

of p

oin

ts o

n a

gra

ph

you

can

det

erm

ine

wh

eth

er t

he

grap

h r

epre

sen

ts a

lin

ear

rela

tion

ship

.

4. C

hoo

se s

ever

al p

airs

of

poin

ts f

rom

th

e gr

aph

at

the

righ

t an

d w

rite

th

e sl

ope-

inte

rcep

t fo

rm o

f th

e li

ne

con

tain

ing

each

pai

r.

S

amp

le a

nsw

er:

y =

x;

y =

2x -

2;

y =

2x +

1

5. W

hat

con

clu

sion

can

you

dra

w f

rom

you

r eq

uat

ion

s in

E

xerc

ise

4? I

s th

is a

lin

e?

T

he

po

ints

are

no

t co

llin

ear.

Th

is is

no

t a

line.

4-3

013_

023_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

2212

/21/

10

12:4

6 A

M


NA

ME

DAT

E

P

ER

IOD

Lesson 4-3

Cha

pte

r 4

23

Gle

ncoe

Alg

ebra

1

Gra

phin

g Ca

lcul

ator

Act

ivit

yW

riti

ng

Lin

ear

Eq

uati

on

s

Lis

ts c

an b

e u

sed

wit

h t

he

lin

ear

regr

essi

on f

un

ctio

n t

o w

rite

an

d ve

rify

li

nea

r eq

uat

ion

s gi

ven

tw

o po

ints

on

a l

ine,

or

the

slop

e of

a l

ine

and

a po

int

thro

ugh

wh

ich

it

pass

es. T

he

lin

ear

regr

essi

on f

un

ctio

n, L

inR

eg (

ax +

b),

is

fou

nd

un

der

the

ST

AT

CA

LC

men

u.

W

rite

th

e sl

ope-

inte

rcep

t fo

rm o

f an

eq

uat

ion

of

the

lin

e th

at p

asse

s th

rou

gh (

3, -

2) a

nd

(6,

4).

En

ter

the

x-co

ordi

nat

es o

f th

e po

ints

in

to L

1 an

d th

e y-

coor

din

ates

in

to L

2. U

se t

he

lin

ear

regr

essi

on f

un

ctio

n t

o w

rite

th

e eq

uat

ion

of

the

lin

e.

Key

stro

kes:

S

TA

T E

NT

ER

3 E

NT

ER

6 E

NT

ER

(

–) 2

EN

TE

R 4

E

NT

ER

S

TA

T

4

2nd

[L

1]

,

2nd

[L

2] E

NT

ER

.T

he

equ

atio

n i

s y

= 2

x -

8.

If y

ou h

ave

alre

ady

wri

tten

th

e eq

uat

ion

of

a li

ne,

you

can

use

th

e gi

ven

in

form

atio

n t

o ve

rify

you

r eq

uat

ion

.

Exer

cise

sW

rite

th

e sl

ope-

inte

rcep

t fo

rm a

nd

th

e st

and

ard

for

m o

f an

eq

uat

ion

of

the

lin

e th

at s

atis

fies

eac

h c

ond

itio

n.

1. p

asse

s th

roug

h (0

, 7)

and

( 1 −

7 ,

-5 )

2.

pas

ses

thro

ugh

(-5,

1),

(10,

10)

, and

(-

10, -

2)

y

= -

84x +

7;

84x +

y =

7

y =

3 −

5 x +

4;

3x -

5y =

- 2

0

3. p

asse

s th

rou

gh (

6, -

4), m

= 2 −

3

4. p

asse

s th

rou

gh (

3, 5

), m

= -

4

y

= 2 −

3 x -

8;

2x -

3y =

24

y =

-4x

+ 1

7; 4

x +

y =

17

5. x

-in

terc

ept:

1, y

-in

terc

ept:

- 1 −

2

6. p

asse

s th

rou

gh (

-18

, 11)

, y-i

nte

rcep

t: 3

y

= 1 −

2 x -

1 −

2 ; x -

2y =

1

y =

- 4 −

9 x +

3;

4x +

9y =

27

V

erif

y th

at t

he

equ

atio

n o

f th

e li

ne

pas

sin

g th

rou

gh (2

, -3)

wit

h s

lop

e -

3 −

4 c

an b

e w

ritt

en a

s 3x

+ 4

y =

-6.

Use

th

e gi

ven

poi

nt

and

slop

e to

det

erm

ine

a se

con

d po

int

thro

ugh

w

hic

h t

he

lin

e pa

sses

. En

ter

the

x-co

ordi

nat

es o

f th

e po

ints

in

to L

1 an

d th

e y-

coor

din

ates

in

to L

2. U

se L

inR

eg (

ax +

b)

to d

eter

min

e th

e sl

ope-

inte

rcep

t fo

rm o

f th

e eq

uat

ion

.

The

slo

pe-i

nter

cept

for

m o

f th

e eq

uati

on i

s y

= -

0.75

x -

1.5

or

y =

- 3 −

4 x

- 3 −

2 .

Th

is c

an b

e re

wri

tten

in

sta

nda

rd f

orm

as

3x +

4y

= -

6.

Exam

ple

1

Exam

ple

2

4-3

013_

023_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

2312

/21/

10

12:4

6 A

M



Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

24

Gle

ncoe

Alg

ebra

1

Stud

y G

uide

and

Inte

rven

tion

Para

llel

an

d P

erp

en

dic

ula

r Lin

es

Para

llel L

ines

Tw

o n

onve

rtic

al l

ines

are

par

alle

l if

th

ey h

ave

the

sam

e sl

ope.

All

ve

rtic

al l

ines

are

par

alle

l.

W

rite

an

eq

uat

ion

in

slo

pe-

inte

rcep

t fo

rm f

or t

he

lin

e th

at p

asse

s th

rou

gh (

-1,

6)

and

is

par

alle

l to

th

e gr

aph

of

y =

2x

+ 1

2.

A l

ine

para

llel

to

y =

2x

+ 1

2 h

as t

he

sam

e sl

ope,

2. R

epla

ce m

wit

h 2

an

d (x

1, y 1)

wit

h

(-1,

6)

in t

he

poin

t-sl

ope

form

.

y -

y1

= m

(x -

x1)

P

oin

t-slo

pe form

y

- 6

= 2

(x -

(-

1))

m =

2; (x

1,

y 1)

= (

-1,

6)

y

- 6

= 2

(x +

1)

Sim

plif

y.

y

- 6

= 2

x +

2

Dis

trib

utive

Pro

pert

y

y

= 2

x +

8

Slo

pe-inte

rcept

form

Th

eref

ore,

th

e eq

uat

ion

is

y =

2x

+ 8

.

Exer

cise

sW

rite

an

eq

uat

ion

in

slo

pe-

inte

rcep

t fo

rm f

or t

he

lin

e th

at p

asse

s th

rou

gh t

he

give

n p

oin

t an

d i

s p

aral

lel

to t

he

grap

h o

f ea

ch e

qu

atio

n.

1.

2.

3.

y

= x

- 4

y

= -

1 −

2 x +

3

y =

4 −

3 x +

7

4. (

-2,

2),

y =

4x

- 2

5.

(6,

4),

y =

1 −

3 x +

1

6. (

4, -

2), y

= -

2x +

3

y

= 4

x +

10

y =

1 −

3 x +

2

y =

-2x

+ 6

7. (

-2,

4),

y =

-3x

+ 1

0 8.

(-

1, 6

), 3x

+ y

= 1

2 9.

(4,

-6)

, x +

2y

= 5

y

= -

3x -

2

y =

-3x

+ 3

y

= -

1 −

2 x -

4

10. F

ind

an e

quat

ion

of

the

lin

e th

at h

as a

y-i

nte

rcep

t of

2 t

hat

is

para

llel

to

the

grap

h o

f th

e li

ne

4x +

2y

= 8

.

11. F

ind

an e

quat

ion

of

the

lin

e th

at h

as a

y-i

nte

rcep

t of

-1

that

is

para

llel

to

the

grap

h o

f th

e li

ne

x -

3y

= 6

.

12. F

ind

an e

quat

ion

of

the

lin

e th

at h

as a

y-i

nte

rcep

t of

-4

that

is

para

llel

to

the

grap

h o

f th

e li

ne

y =

6.

( –3,

3)

x

y

O

4x -

3y

= –

12

( -8,

7)

x

y

O

y =

- x

- 4

1 2

2

2

( 5, 1

)x

y

O

y =

x -

8

Exam

ple

y =

-2x

+ 2

y =

1 −

3 x -

1

y =

-4

4-4

024_

035_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

2412

/21/

10

12:4

6 A

M


NA

ME

DAT

E

P

ER

IOD

Lesson 4-4

Cha

pte

r 4

25

Gle

ncoe

Alg

ebra

1

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Para

llel

an

d P

erp

en

dic

ula

r Lin

es

Perp

end

icu

lar

Lin

es T

wo

non

vert

ical

lin

es a

re p

erp

end

icu

lar

if t

hei

r sl

opes

are

n

egat

ive

reci

proc

als

of e

ach

oth

er. V

erti

cal

and

hor

izon

tal

lin

es a

re p

erpe

ndi

cula

r.

Wri

te a

n e

qu

atio

n i

n s

lop

e-in

terc

ept

form

for

th

e li

ne

that

pas

ses

thro

ugh

(-

4, 2

) an

d i

s p

erp

end

icu

lar

to t

he

grap

h o

f 2x

- 3

y =

9.

Fin

d th

e sl

ope

of 2

x -

3y

= 9

. 2

x -

3y

= 9

O

rigin

al equation

-3y

= -

2x +

9

Subtr

act

2x

from

each s

ide.

y =

2 −

3 x -

3

Div

ide e

ach s

ide b

y -

3.

Th

e sl

ope

of y

= 2 −

3 x -

3 i

s 2 −

3 . S

o, t

he

slop

e of

th

e li

ne

pass

ing

thro

ugh

(-

4, 2

) th

at i

s pe

rpen

dicu

lar

to t

his

lin

e is

th

e n

egat

ive

reci

proc

al o

f 2 −

3 , or

-

3 −

2 .U

se t

he

poin

t-sl

ope

form

to

fin

d th

e eq

uat

ion

.y

- y

1 =

m(x

- x

1)

Poin

t-slo

pe form

y -

2 =

-

3 −

2 (x -

(-

4))

m =

-

3

−

2 ;

(x1,

y 1)

= (

-4,

2)

y -

2 =

-

3 −

2 (x +

4)

Sim

plif

y.

y

- 2

= -

3 −

2 x -

6

Dis

trib

utive

Pro

pert

y

y

= -

3 −

2 x -

4

Slo

pe-inte

rcept

form

Exer

cise

s 1

. AR

CH

ITEC

TUR

E O

n t

he

arch

itec

t’s p

lan

s fo

r a

new

hig

h s

choo

l, a

wal

l re

pres

ente

d by

−−

−

M

N h

as e

ndp

oin

ts M

(-3,

-1

) a

nd

N

(2,

1). A

wal

l re

pres

ente

d by

−−

−

P

Q h

as e

ndp

oin

ts

P(4

, -4)

an

d Q

(-2,

11)

. Are

th

e w

alls

per

pen

dicu

lar?

Exp

lain

.

Y

es, b

ecau

se t

he

slo

pe

of

−−

M

N (

2 −

5 ) is

th

e n

egat

ive

reci

pro

cal o

f th

e sl

op

e

of

−−

P

Q (

- 5 −

2 ) .

Det

erm

ine

wh

eth

er t

he

grap

hs

of t

he

foll

owin

g eq

uat

ion

s ar

e p

ara

llel

or

per

pen

dic

ula

r.

2. 2

x +

y

= -

7, x

- 2y

= -

4, 4x

- y

= 5

fi

rst

two

are

per

pen

dic

ula

r

3. y

= 3x,

6x

- 2y

= 7

, 3y

= 9x

- 1

al

l are

par

alle

l

Wri

te a

n e

qu

atio

n i

n s

lop

e-in

terc

ept

form

for

th

e li

ne

that

pas

ses

thro

ugh

th

e gi

ven

poi

nt

and

is

per

pen

dic

ula

r to

th

e gr

aph

of

each

eq

uat

ion

.

4. (

4, 2

), y

= 1 −

2 x +

1

5. (

2, -

3), y

= -

2 −

3 x +

4

6. (

6, 4

), y

= 7

x +

1

y

= -

2x +

10

y =

3 −

2 x -

6

y =

- 1 −

7 x +

34

−

7

7. (

-8,

-7)

, y =

-x

- 8

8.

(6,

-2)

, y =

-3x

- 6

9.

(-

5, -

1), y

= 5 −

2 x -

3

y

= x

+ 1

y

= 1 −

3 x -

4

y =

- 2 −

5 x -

3

Exam

ple

4-4

024_

035_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

2512

/21/

10

12:4

6 A

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

26

Gle

ncoe

Alg

ebra

1

Skill

s Pr

acti

ceP

ara

llel

an

d P

erp

en

dic

ula

r Lin

es

Wri

te a

n e

qu

atio

n i

n s

lop

e-in

terc

ept

form

for

th

e li

ne

that

pas

ses

thro

ugh

th

e gi

ven

poi

nt

and

is

par

alle

l to

th

e gr

aph

of

the

give

n e

qu

atio

n.

1.

2.

3.

y

= 2

x +

1

y =

-x

y =

1 −

2 x +

3

4. (

3, 2

), y

= 3

x +

4

5. (

-1,

-2)

, y =

-3x

+ 5

6.

(-

1, 1

), y

= x

- 4

y

= 3

x -

7

y =

-3x

- 5

y

= x

+ 2

7. (

1, -

3), y

= -

4x -

1

8. (

-4,

2),

y =

x +

3

9. (

-4,

3),

y =

1 −

2 x -

6

y

= -

4x +

1

y =

x +

6

y =

1 −

2 x +

5

10. R

AD

AR

On

a r

adar

scr

een

, a p

lan

e lo

cate

d at

A(-

2, 4

) is

fly

ing

tow

ard

B(4

, 3

).

An

oth

er p

lan

e, l

ocat

ed a

t C

(-

3, 1

), is

fly

ing

tow

ard

D(3,

0

). A

re t

he

plan

es’ p

ath

s pe

rpen

dicu

lar?

Exp

lain

.

N

o;

the

slo

pes

are

eq

ual

, mea

nin

g t

he

pat

hs

are

par

alle

l.

Det

erm

ine

wh

eth

er t

he

grap

hs

of t

he

foll

owin

g eq

uat

ion

s ar

e p

ara

llel

or

per

pen

dic

ula

r. E

xpla

in.

11.

y =

2 −

3 x +

3,

y

= 3 −

2 x, 2

x -

3y

= 8

fi

rst

an

d t

hir

d a

re p

aral

lel;

slo

pes

are

eq

ual

12.

y

= 4

x, x

+ 4

y =

12,

4x

+ y

= 1

fi

rst

an

d s

eco

nd

are

per

pen

dic

ula

r; s

lop

es a

re n

egat

ive

reci

pro

cals

Wri

te a

n e

qu

atio

n i

n s

lop

e-in

terc

ept

form

for

th

e li

ne

that

pas

ses

thro

ugh

th

e gi

ven

poi

nt

and

is

per

pen

dic

ula

r to

th

e gr

aph

of

the

give

n e

qu

atio

n.

13. (

-3,

-2)

, y =

x +

2

14. (

4, -

1), y

= 2

x -

4

15. (

-1,

-6)

, x +

3y

= 6

y

= -

x -

5

y =

- 1 −

2 x +

1

y =

3x -

3

16. (

-4,

5),

y =

-4x

- 1

17

. (-

2, 3

), y

=

1 −

4 x -

4

18. (

0, 0

), y

=

1 −

2 x -

1

y

= 1 −

4 x +

6

y =

-4x

- 5

y

= -

2x

( –2,

2)

x

y O

y =

1 2x

+ 1

( 1, –

1)

x

y

O

y =

–x

+ 3

( –2,

–3)

x

y O

y =

2x

- 1

4-4

024_

035_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

2612

/21/

10

12:4

6 A

M


NA

ME

DAT

E

P

ER

IOD

Lesson 4-4

Cha

pte

r 4

27

Gle

ncoe

Alg

ebra

1

Prac

tice

P

ara

llel

an

d P

erp

en

dic

ula

r Lin

es

Wri

te a

n e

qu

atio

n i

n s

lop

e-in

terc

ept

form

for

th

e li

ne

that

pas

ses

thro

ugh

th

e gi

ven

poi

nt

and

is

par

alle

l to

th

e gr

aph

of

the

give

n e

qu

atio

n.

1. (

3, 2

), y

= x

+ 5

2.

(-

2, 5

), y

= -

4x +

2

3. (

4, -

6), y

= -

3

−

4

x

+ 1

y

= x

- 1

y

= -

4x -

3

y =

-

3 −

4 x -

3

4. (

5, 4

), y

= 2 −

5 x -

2

5. (

12, 3

), y

= 4 −

3 x +

5

6. (

3, 1

), 2x

+ y

= 5

y

= 2 −

5 x +

2

y =

4 −

3 x -

13

y =

-2x

+ 7

7. (

-3,

4),

3y =

2x

- 3

8.

(-

1, -

2), 3

x -

y =

5

9. (

-8,

2),

5x -

4y

= 1

y

= 2 −

3 x +

6

y =

3x +

1

y =

5 −

4 x +

12

10. (

-1,

-4)

, 9x

+ 3

y =

8

11. (

-5,

6),

4x +

3y

= 1

12

. (3,

1),

2x +

5y

= 7

y

= -

3x -

7

y =

-

4 −

3 x -

2 −

3 y

= -

2 −

5 x +

11

−

5

Wri

te a

n e

qu

atio

n i

n s

lop

e-in

terc

ept

form

for

th

e li

ne

that

pas

ses

thro

ugh

th

e gi

ven

poi

nt

and

is

per

pen

dic

ula

r to

th

e gr

aph

of

the

give

n e

qu

atio

n.

13. (

-2,

-2)

, y =

-

1

−

3

x

+ 9

14

. (-

6, 5

), x

- y

= 5

15

. (-

4, -

3), 4

x +

y =

7

y

= 3

x +

4

y =

-x -

1

y =

1 −

4 x -

2

16. (

0, 1

), x

+ 5

y =

15

17. (

2, 4

), x

- 6

y =

2

18. (

-1,

-7)

, 3x

+ 1

2y =

-6

y

= 5

x +

1

y =

-6x

+ 1

6 y

= 4

x -

3

19. (

-4,

1),

4x +

7y

= 6

20

. (10

, 5),

5x +

4y

= 8

21

. (4,

-5)

, 2x

- 5

y =

-10

y

= 7 −

4 x +

8

y =

4 −

5 x -

3

y =

-

5 −

2 x +

5

22. (

1, 1

), 3x

+ 2

y =

-7

23. (

-6,

-5)

, 4x

+ 3

y =

-6

24. (

-3,

5),

5x -

6y

= 9

y

= 2 −

3 x +

1 −

3 y

= 3 −

4 x -

1 −

2 y

= -

6 −

5 x +

7 −

5

25. G

EOM

ETRY

Qu

adri

late

ral

AB

CD

has

dia

gon

als

−−

A

C a

nd

−−

−

B

D .

D

eter

min

e w

het

her

−−

A

C i

s pe

rpen

dicu

lar

to −

−−

B

D . E

xpla

in.

Y

es;

they

are

per

pen

dic

ula

r b

ecau

se t

hei

r sl

op

es a

re

7

an

d -

1 −

7 , w

hic

h a

re n

egat

ive

reci

pro

cals

.

26. G

EOM

ETRY

Tri

angl

e A

BC

has

ver

tice

s A

(0, 4

), B

(1, 2

), an

d C

(4, 6

). D

eter

min

e w

het

her

tr

ian

gle

AB

C i

s a

righ

t tr

ian

gle.

Exp

lain

.

Y

es;

sid

es −

−

A

B a

nd

−−

A

C a

re p

erp

end

icu

lar

bec

ause

th

eir

slo

pes

are

-2

and

1 −

2 , w

hic

h a

re n

egat

ive

reci

pro

cals

.

x

y O

A

D

C

B

4-4

024_

035_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

2712

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10

12:4

6 A

M



Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

28

Gle

ncoe

Alg

ebra

1

1.B

USI

NES

S B

rady

’s B

ooks

is

a re

tail

st

ore.

Th

e st

ore’

s av

erag

e da

ily

prof

its

y ar

e gi

ven

by

the

equ

atio

n y

= 2

x +

3

wh

ere

x is

th

e n

um

ber

of h

ours

ava

ilab

le

for

cust

omer

pu

rch

ases

. Bra

dy’s

add

s an

on

lin

e sh

oppi

ng

opti

on. W

rite

an

eq

uat

ion

in

slo

pe-i

nte

rcep

t fo

rm t

o sh

ow

a n

ew p

rofi

t li

ne

wit

h t

he

sam

e pr

ofit

ra

te c

onta

inin

g th

e po

int

(0, 1

2).

y =

2x +

12

2.A

RC

HIT

ECTU

RE

Th

e fr

ont

view

of

a h

ouse

is

draw

n o

n g

raph

pap

er. T

he

left

si

de o

f th

e ro

of o

f th

e h

ouse

is

repr

esen

ted

by t

he

equ

atio

n y

= x

. Th

e ro

ofli

nes

in

ters

ect

at a

rig

ht

angl

e an

d th

e pe

ak o

f th

e ro

of i

s re

pres

ente

d by

th

e po

int

(5, 5

). W

rite

th

e eq

uat

ion

in

slo

pe-

inte

rcep

t fo

rm f

or t

he

lin

e th

at c

reat

es

the

righ

t si

de o

f th

e ro

of.

y =

-x +

10

3. A

RC

HA

EOLO

GY

An

arc

hae

olog

ist

is

com

pari

ng

the

loca

tion

of

a je

wel

ed b

ox

she

just

fou

nd

to t

he

loca

tion

of

a br

ick

wal

l. T

he

wal

l ca

n b

e re

pres

ente

d by

th

e

equ

atio

n y

= -

5 −

3 x +

13.

Th

e bo

x is

loc

ated

at

the

poin

t (1

0, 9

). W

rite

an

eq

uat

ion

rep

rese

nti

ng

a li

ne

that

is

perp

endi

cula

r to

th

e w

all

and

that

pas

ses

thro

ugh

th

e lo

cati

on o

f th

e bo

x.

y

= 3 −

5 x +

3

4.G

EOM

ETRY

A p

aral

lelo

gram

is

crea

ted

by t

he

inte

rsec

tion

s of

th

e li

nes

x=

2,

x

= 6

, y =

1 −

2 x +

2, a

nd

anot

her

lin

e. F

ind

t

he

equ

atio

n o

f th

e fo

urt

h l

ine

nee

ded

to

com

plet

e th

e pa

rall

elog

ram

. Th

e li

ne

shou

ld p

ass

thro

ugh

(2,

0).

(H

int:

Ske

tch

a

grap

h t

o h

elp

you

see

th

e li

nes

.)

y =

1 −

2 x -

1

5. IN

TER

IOR

DES

IGN

Pam

ela

is p

lan

nin

g to

in

stal

l an

isl

and

in h

er k

itch

en.

Sh

e dr

aws

the

shap

e sh

e li

kes

by c

onn

ecti

ng

the

vert

ices

of

the

squ

are

tile

s on

her

ki

tch

en f

loor

. Sh

e re

cord

s th

e lo

cati

on o

f ea

ch c

orn

er i

n t

he

tabl

e.

a. H

ow m

any

pair

s of

par

alle

l si

des

are

ther

e in

th

e sh

ape

AB

CD

sh

e de

sign

ed?

Exp

lain

.

1 p

air:

−−

B

C a

nd

−−

A

D a

re p

aral

lel

bec

ause

th

eir

slo

pes

are

bo

th

0.5.

b.

How

man

y pa

irs

of p

erpe

ndi

cula

r si

des

are

ther

e in

th

e sh

ape

she

desi

gned

? E

xpla

in.

2

pai

rs:

−−

B

C ⊥

−−

A

B a

nd

−−

A

B ⊥

−−

A

D

bec

ause

−−

A

B h

as a

slo

pe

of

-2,

w

hic

h is

th

e o

pp

osi

te r

ecip

roca

l o

f th

e sl

op

es o

f −

−

B

C a

nd

−−

A

D , 0

.5.

c. W

hat

is

the

shap

e of

her

new

isl

and?

a

trap

ezo

id

Wor

d Pr

oble

m P

ract

ice

Para

llel

an

d P

erp

en

dic

ula

r Lin

es

y

xO

( 5, 5

)

Co

rner

Dis

tan

ce

fro

m W

est

Wal

l (ti

les)

Dis

tan

ce

fro

m S

ou

th

Wal

l (ti

les)

A5

4

B3

8

C7

10

D11

7

4-4

024_

035_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

2812

/21/

10

12:4

6 A

M


NA

ME

DAT

E

P

ER

IOD

Lesson 4-4

Cha

pte

r 4

29

Gle

ncoe

Alg

ebra

1

Enri

chm

ent

Pen

cils o

f Lin

es

All

of

the

lin

es t

hat

pas

s th

rou

gh

a si

ngl

e po

int

in t

he

sam

e pl

ane

are

call

ed a

pen

cil o

f li

nes

.A

ll l

ines

wit

h t

he

sam

e sl

ope,

bu

t di

ffer

ent

inte

rcep

ts, a

re a

lso

call

ed a

“pe

nci

l,” a

pen

cil o

f p

aral

lel l

ines

.

Gra

ph

som

e of

th

e li

nes

in

eac

h p

enci

l.

1. A

pen

cil

of l

ines

th

rou

gh t

he

2.

A p

enci

l of

lin

es d

escr

ibed

by

po

int

(1, 3

) y

- 4

= m

(x -

2),

wh

ere

m i

s an

y re

al n

um

ber

3. A

pen

cil

of l

ines

par

alle

l to

th

e li

ne

4.

A p

enci

l of

lin

es d

escr

ibed

by

x

- 2

y =

7

y =

mx

+ 3

m -

2 ,

wh

ere

m i

s an

y re

al n

um

ber

x

y

Ox

y

O

x

y

Ox

y

O

4-4

024_

035_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

2912

/21/

10

12:4

6 A

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF 2nd



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

30

Gle

ncoe

Alg

ebra

1

Stud

y G

uide

and

Inte

rven

tion

Scatt

er

Plo

ts a

nd

Lin

es o

f Fit

Inve

stig

ate

Rel

atio

nsh

ips

Usi

ng

Sca

tter

Plo

ts A

sca

tter

plo

t is

a g

raph

in

w

hic

h t

wo

sets

of

data

are

plo

tted

as

orde

red

pair

s in

a c

oord

inat

e pl

ane.

If

y in

crea

ses

as x

in

crea

ses,

th

ere

is a

pos

itiv

e co

rrel

atio

n b

etw

een

x a

nd

y. I

f y

decr

ease

s as

x i

ncr

ease

s,

ther

e is

a n

egat

ive

corr

elat

ion

bet

wee

n x

an

d y.

If

x an

d y

are

not

rel

ated

, th

ere

is n

o co

rrel

atio

n.

EA

RN

ING

S T

he

grap

h a

t th

e ri

ght

show

s th

e am

oun

t of

mon

ey C

arm

en e

arn

ed e

ach

w

eek

an

d t

he

amou

nt

she

dep

osit

ed i

n h

er s

avin

gs

acco

un

t th

at s

ame

wee

k. D

eter

min

e w

het

her

th

e gr

aph

sh

ows

a p

osit

ive

corr

ela

tion

, a n

ega

tive

co

rrel

ati

on, o

r n

o co

rrel

ati

on. I

f th

ere

is a

p

osit

ive

or n

egat

ive

corr

elat

ion

, des

crib

e it

s m

ean

ing

in t

he

situ

atio

n.

Th

e gr

aph

sh

ows

a po

siti

ve c

orre

lati

on. T

he

mor

e C

arm

en e

arn

s, t

he

mor

e sh

e sa

ves.

Exer

cise

sD

eter

min

e w

het

her

eac

h g

rap

h s

how

s a

pos

itiv

e co

rrel

ati

on, a

neg

ati

ve

corr

ela

tion

, or

no

corr

ela

tion

. If

ther

e is

a p

osit

ive

or n

egat

ive

corr

elat

ion

, d

escr

ibe

its

mea

nin

g in

th

e si

tuat

ion

.

1.

2.

Neg

ativ

e co

rrel

atio

n;

as t

ime

incr

ease

s,

spee

d

dec

reas

es.

3.

4.

Ave

rage

Wee

kly

Wor

k H

ours

in U

.S.

Hours

34.0

34.2

33.8

33.6

34.4

34.6

Year

s Si

nce

1995

32

10

54

76

98

Sour

ce: T

he W

orld

Alm

anac

Ave

rage

Jogg

ing

Spee

d

Min

utes

Miles per Hour

010

205

1525

10 5

Carm

en’s

Ear

ning

s an

d Sa

ving

s

Dolla

rs E

arne

d

Dollars Saved

040

8012

0

35 30 25 20 15 10 5

no

co

rrel

atio

n

Exam

ple

Po

siti

ve

corr

elat

ion

; as

yea

rs

incr

ease

, th

e av

erag

e w

eekl

y w

ork

ho

urs

al

so

incr

ease

.

Po

siti

ve

corr

elat

ion

; as

yea

rs

incr

ease

, th

e am

ou

nt

of

imp

ort

s al

so

incr

ease

.

Ave

rage

U.S

. Hou

rly

Earn

ings

Hourly Earnings ($)

15 016171819

Year

s Si

nce

2003

Sour

ce: U

.S. D

ept.

of L

abor

12

34

5

U.S.

Impo

rts

from

Mex

ico

Imports ($ billions) 130 0

160

190

220

Year

s Si

nce

2003

Sour

ce: U

.S. C

ensu

s Bur

eau

12

34

5

4-5

024_

035_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

3012

/23/

10

7:06

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 4-5

Cha

pte

r 4

31

Gle

ncoe

Alg

ebra

1

Use

Lin

es o

f Fi

t

T

he

tab

le s

how

s th

e n

um

ber

of

stu

den

ts p

er c

omp

ute

r in

Eas

ton

H

igh

Sch

ool

for

cert

ain

sch

ool

year

s fr

om 1

996

to 2

008.

Year

19

96

19

98

20

00

20

02

20

04

20

06

20

08

Stu

den

ts p

er C

om

pu

ter

22

18

14

10

6.1

5.4

4.9

a. D

raw

a s

catt

er p

lot

and

det

erm

ine

w

hat

rel

atio

nsh

ip e

xist

s, i

f an

y.S

ince

y d

ecre

ases

as

x in

crea

ses,

th

e co

rrel

atio

n i

s n

egat

ive.

b.

Dra

w a

lin

e of

fit

for

th

e sc

atte

r p

lot.

Dra

w a

lin

e th

at p

asse

s cl

ose

to m

ost

of t

he

poin

ts.

A l

ine

of f

it i

s sh

own

.c.

Wri

te t

he

slop

e-in

terc

ept

form

of

an e

qu

atio

n

for

the

lin

e of

fit

.T

he

lin

e of

fit

sh

own

pas

ses

thro

ugh

(1

999,

16)

an

d (2

005,

5.7

). F

ind

the

slop

e.

m

=

5.7

- 1

6

−

20

05

-

19

99

m

= -

1.7

F

ind

b in

y =

-1.

7x +

b.

16

= -

1.7

· 1

993

+ b

34

04 =

b

Th

eref

ore,

an

equ

atio

n o

f a

lin

e of

fit

is

y =

-1.

7x +

340

4.

Exer

cise

sR

efer

to

the

tab

le f

or E

xerc

ises

1–3

.

1. D

raw

a s

catt

er p

lot.

2. D

raw

a l

ine

of f

it f

or t

he

data

.

3. W

rite

th

e sl

ope-

inte

rcep

tfo

rm o

f an

equ

atio

n f

or t

he

lin

e of

fit

.

T

he

po

ints

(0,

5.0

8)

and

(3,

5.8

1) g

ive

y =

0.2

43x +

5.0

8 as

a li

ne

of

fi t.

Mov

ie A

dmis

sion

Pri

ces

Admission ($)

5.4

5.6

5.2 5

5.86

6.2

Year

s Si

nce

1999

32

10

54

Sour

ce: U

.S. C

ensu

s B

urea

u

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Scatt

er

Plo

ts a

nd

Lin

es o

f Fit

Stud

ents

per

Com

pute

rin

Eas

ton

Hig

h Sc

hool

Students per Computer

81216 4 02024

Year

1996

1998

2000

2002

2004

2006

2008

Exam

ple

Year

s S

ince

199

9A

dm

issi

on

(d

olla

rs)

0$

5.0

8

1$

5.3

9

2$

5.6

6

3$

5.8

1

4$

6.0

3

4-5

024_

035_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

3112

/23/

10

12:3

3 P

M


A13-A24_ALG1_A_CRM_C04_AN_660499.indd A14A13-A24_ALG1_A_CRM_C04_AN_660499.indd A14 12/23/10 7:09 PM12/23/10 7:09 PM

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

32

Gle

ncoe

Alg

ebra

1

Skill

s Pr

acti

ceS

catt

er

Plo

ts a

nd

Lin

es o

f Fit

Det

erm

ine

wh

eth

er e

ach

gra

ph

sh

ows

a p

osit

ive

corr

ela

tion

, a n

ega

tive

co

rrel

ati

on, o

r n

o co

rrel

ati

on. I

f th

ere

is a

pos

itiv

e or

neg

ativ

e co

rrel

atio

n,

des

crib

e it

s m

ean

ing

in t

he

situ

atio

n.

1.

2.

P

osi

tive

; th

e lo

ng

er t

he

exer

cise

, n

o c

orr

elat

ion

th

e m

ore

Cal

ori

es b

urn

ed.

3.

4.

N

egat

ive;

as

wei

gh

t in

crea

ses,

P

osi

tive

; as

th

e ye

ar in

crea

ses,

th

e n

um

ber

of

rep

etit

ion

s

th

e d

eale

rsh

ip’s

rev

enu

ed

ecre

ases

.

in

crea

ses

5. B

ASE

BA

LL T

he

scat

ter

plot

sh

ows

the

aver

age

pric

e of

a m

ajor

-lea

gue

base

ball

tic

ket

from

199

7 to

200

6.

a.

Det

erm

ine

wh

at r

elat

ion

ship

, if

any,

exi

sts

in t

he

data

. Exp

lain

. P

osi

tive

; as

th

e ye

ar

incr

ease

s, t

he

pri

ce in

crea

ses.

b.

Use

th

e po

ints

(19

98, 1

3.60

) an

d (2

003,

19.

00)

to w

rite

th

e sl

ope-

inte

rcep

t fo

rm o

f an

equ

atio

n f

or

the

lin

e of

fit

sh

own

in

th

e sc

atte

r pl

ot.

y =

1.0

8x -

214

4.24

c.

Pre

dict

th

e pr

ice

of a

tic

ket

in 2

009.

ab

ou

t $2

5.48

Wei

ght-

Lift

ing

Wei

ght (

poun

ds)

Repetitions

040

8020

6010

012

014

0

14 12 10 8 6 4 2

Libr

ary

Fine

s

Book

s Bo

rrow

ed

Fines (dollars)

02

45

67

89

13

10

7 6 5 4 3 2 1

Calo

ries

Bur

ned

Dur

ing

Exer

cise

Tim

e (m

inut

es)

Calories

020

4010

3050

60

600

500

400

300

200

100

Base

ball

Tick

et P

rice

s

Average Price ($)

1416 12 018202224

Year

’99

’98

’97

’01

’03

’00

Sour

ce: T

eam

Mar

ketin

g Re

port,

Chi

cago

’02

’04

’05

’06

Car

Dea

lers

hip

Reve

nue

Revenue(hundreds of thousands)

46 2 08101214

Year

’99

’01

’03

’00

’02

’04

’05

’06

’07

’08

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024_

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NA

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DAT

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Lesson 4-5

Cha

pte

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Gle

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Alg

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1

Prac

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S

catt

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Plo

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Lin

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Det

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wh

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ach

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sh

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a p

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corr

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co

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f th

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des

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s m

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in t

he

situ

atio

n.

1.

2.

n

o c

orr

elat

ion

3. D

ISEA

SE T

he

tabl

e sh

ows

the

nu

mbe

r of

cas

es o

f F

oodb

orn

e B

otu

lism

in

th

e U

nit

ed S

tate

s fo

r th

e ye

ars

2001

to

2005

.

a.

Dra

w a

sca

tter

plo

t an

d de

term

ine

wh

at

rela

tion

ship

, if

any,

exi

sts

in t

he

data

.

Neg

ativ

e co

rrel

atio

n;

as t

he

year

in

crea

ses,

th

e n

um

ber

of

case

s d

ecre

ases

.

b. D

raw

a l

ine

of f

it f

or t

he

scat

ter

plot

.

Sam

ple

an

swer

giv

en.

c.

Wri

te t

he

slop

e-in

terc

ept

form

of

an e

quat

ion

for

th

e li

ne

of f

it.

Sam

ple

an

swer

: y =

-12

9.75

x +

906

4. Z

OO

S T

he

tabl

e sh

ows

the

aver

age

and

max

imu

m

lon

gevi

ty o

f va

riou

s an

imal

s in

cap

tivi

ty.

a. D

raw

a s

catt

er p

lot

and

dete

rmin

e w

hat

re

lati

onsh

ip, i

f an

y, e

xist

s in

th

e da

ta.

P

osi

tive

co

rrel

atio

n;

as t

he

aver

age

incr

ease

s, t

he

max

imu

m in

crea

ses.

b.

Dra

w a

lin

e of

fit

for

th

e sc

atte

r pl

ot.

Sam

ple

an

swer

: U

se (

15, 4

0), (

35, 7

0).

c. W

rite

th

e sl

ope-

inte

rcep

t fo

rm o

f an

equ

atio

n f

or t

he

lin

e of

fit

. S

amp

le a

nsw

er:

y =

1.5

x +

17.

5

d.

Pre

dict

th

e m

axim

um

lon

gevi

ty f

or a

n a

nim

al w

ith

an

ave

rage

lon

gevi

ty o

f 33

yea

rs.

abo

ut

67 y

r

Stat

e El

evat

ions

Mea

n El

evat

ion

(feet

)

Highest Point(thousands of feet)

1000

020

0030

00

16 12 8 4

Sour

ce: U

.S. G

eolo

gica

l Sur

vey

Tem

pera

ture

ver

sus

Rain

fall

Aver

age

Annu

al R

ainf

all (

inch

es)

AverageTemperature (ºF)

1015

2025

3035

4045

64 60 56 52 0

Sour

ce: N

atio

nal O

cean

ic a

nd A

tmos

pher

icAd

min

istr

atio

n

U.S.

Foo

dbor

neBo

tulis

m C

ases

Cases

2030 10 04050

Year

2001

2002

2003

2004

2005

Ani

mal

Lon

gevi

ty (Y

ears

)

Aver

age

Maximum

50

1015

2025

3035

4045

80 70 60 50 40 30 20 10

Sour

ce: C

ente

rs fo

r D

isea

se C

ontr

ol

U.S

. Fo

od

bo

rne

Bo

tulis

m C

ases

Year

20

01

20

02

20

03

20

04

20

05

Cas

es3

92

82

016

18

Sour

ce: W

alke

r’s M

amm

als

of t

he W

orld

Lo

ng

evit

y (y

ears

)

Avg

.12

25

15

83

54

04

12

0

Max

.4

75

04

02

07

07

76

15

4

Po

siti

ve;

as t

he

mea

n

elev

atio

n in

crea

ses,

th

e h

igh

est

po

int

incr

ease

s.

4-5

024_

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ALG

1_A

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6049

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Co

pyrig

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cGraw

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cGraw

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PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

34

Gle

ncoe

Alg

ebra

1

1.M

USI

C T

he

scat

ter

plot

sh

ows

the

nu

mbe

r of

CD

s in

mil

lion

s th

at w

ere

sold

fr

om 1

999

to 2

005.

If

the

tren

d co

nti

nu

ed, a

bou

t h

ow m

any

CD

s w

ere

sold

in

200

6?

Sam

ple

an

swer

: ar

ou

nd

70

0 m

illio

n

2. F

AM

ILY

Th

e ta

ble

show

s th

e pr

edic

ted

ann

ual

cos

t fo

r a

mid

dle

inco

me

fam

ily

to

rais

e a

chil

d fr

om b

irth

un

til

adu

lth

ood.

D

raw

a s

catt

er p

lot

and

desc

ribe

wh

at

rela

tion

ship

exi

sts

wit

hin

th

e da

ta.

T

her

e is

a p

osi

tive

co

rrel

atio

n

bet

wee

n t

he

child

’s a

ge

and

an

nu

al c

ost

.

3.H

OU

SIN

G T

he

med

ian

pri

ce o

f an

ex

isti

ng

hom

e w

as $

160,

000

in 2

000

and

$240

,000

in

200

7. I

f x

repr

esen

ts t

he

nu

mbe

r of

yea

rs s

ince

200

0, u

se t

hes

e da

ta p

oin

ts t

o de

term

ine

a li

ne

of b

est

fit

for

the

tren

ds i

n t

he

pric

e of

exi

stin

g h

omes

. Wri

te t

he

equ

atio

n i

n s

lope

-in

terc

ept

form

.

y

= 1

1,42

8.6x

+ 1

60,0

00

4.B

ASE

BA

LL T

he

tabl

e sh

ows

the

aver

age

len

gth

in

min

ute

s of

pro

fess

ion

al

base

ball

gam

es i

n s

elec

ted

year

s.

Sour

ce: E

lias

Spor

ts B

urea

u

a. D

raw

a s

catt

er p

lot

and

dete

rmin

e w

hat

rel

atio

nsh

ip, i

f an

y, e

xist

s in

th

e da

ta.

no

co

rrel

atio

n

b.

Exp

lain

wh

at t

he

scat

ter

plot

sh

ows.

Th

ere

is n

o c

on

sist

ent

tren

d

reg

ard

ing

th

e le

ng

th o

f g

ames

.

c. D

raw

a l

ine

of f

it f

or t

he

scat

ter

plot

.

See

lin

e o

f fi t

on

sca

tter

plo

t ab

ove.Time (min) 16

6 0

168

170

172

174

176

178

180

Year

’90

’92

’94

’96

’98

’00

’02

Ag

e (y

ears

)3

06

1215

y

x9

Annual Cost ($1000)

1112 10 91316 15 1417

Sou

rce:

The

Wor

ld A

lman

ac

Sou

rce:

RIA

A

Year

‘01

‘00

‘99

0‘0

3‘0

2‘0

5

y

x‘0

4

CDs (millions)

750

800

700

650

850

950

900W

ord

Prob

lem

Pra

ctic

eS

catt

er

Plo

ts a

nd

Lin

es o

f Fit

Co

st o

f R

aisi

ng

a C

hild

Bo

rn in

20

03

Ch

ild’s

A

ge

36

912

15

An

nu

al

Co

st (

$)10

,70

011

,70

012

,60

015

,00

016

,70

0

Ave

rag

e L

eng

th o

f M

ajo

r L

eag

ue

Bas

ebal

l Gam

es

Year

‘92

‘94

‘96

‘98

‘00

‘02

‘04

Tim

e (m

in)

17

0174

17

116

817

817

216

7

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6049

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M


NA

ME

DAT

E

P

ER

IOD

Lesson 4-5

Cha

pte

r 4

35

Gle

ncoe

Alg

ebra

1

Enri

chm

ent

Lati

tud

e a

nd

Tem

pera

ture

Th

e la

titu

de

of a

pla

ce o

n E

arth

is

th

e m

easu

re o

f it

s di

stan

ce f

rom

the

equ

ator

. Wh

at d

o yo

u t

hin

k is

th

e re

lati

onsh

ip b

etw

een

a c

ity’

s la

titu

de a

nd

its

mea

n J

anu

ary

tem

pera

ture

? A

t th

e ri

ght

is a

ta

ble

con

tain

ing

the

lati

tude

s an

d Ja

nu

ary

mea

n t

empe

ratu

res

for

fift

een

U.S

. cit

ies.

Sam

ple

an

swer

s ar

e g

iven

.

Sour

ces:

Nat

iona

l Wea

ther

Ser

vice

1. U

se t

he

info

rmat

ion

in

th

e ta

ble

to c

reat

e a

scat

ter

plot

an

d dr

aw a

lin

e of

bes

t fi

t fo

r th

e da

ta.

2. W

rite

an

equ

atio

n f

or t

he

lin

e of

fit

. Mak

e a

con

ject

ure

abo

ut

the

rela

tion

ship

be

twee

n a

cit

y’s

lati

tude

an

d it

s m

ean

Ja

nu

ary

tem

pera

ture

.

S

amp

le a

nsw

er:

y =

-2.

39x +

121

.86;

Th

e h

igh

er t

he

lati

tud

e, t

he

low

er t

he

tem

per

atu

re.

3. U

se y

our

equ

atio

n t

o pr

edic

t th

e Ja

nu

ary

mea

n t

empe

ratu

re o

f Ju

nea

u, A

lask

a, w

hic

h h

as l

atit

ude

58:

23 N

. -

17.7

º F

4. W

hat

wou

ld y

ou e

xpec

t to

be

the

lati

tude

of

a ci

ty w

ith

a J

anu

ary

mea

n t

empe

ratu

re

of 1

5°F

? 44

:42

N

5. W

as y

our

con

ject

ure

abo

ut

the

rela

tion

ship

bet

wee

n l

atit

ude

an

d te

mpe

ratu

re c

orre

ct?

Y

es;

as t

he

lati

tud

e in

crea

ses,

th

e te

mp

erat

ure

dec

reas

es.

6. R

esea

rch

th

e la

titu

des

and

tem

pera

ture

s fo

r ci

ties

in

th

e so

uth

ern

hem

isph

ere.

Doe

s yo

ur

con

ject

ure

hol

d fo

r th

ese

citi

es a

s w

ell?

Yes

.

Lati

tud

e (º

N)

Temperature (ºF)

70 60 50 40 30 20 10 0

-10T

L20

4060

1030

50

U.S

. Cit

yL

atitu

de

Jan

uar

y M

ean

Tem

per

atu

re

Alb

any,

New

Yo

rk4

2:4

0 N

20

.7°F

Alb

uq

ue

rqu

e,

New

Mexic

o3

5:0

7 N

34

.3°F

An

ch

ora

ge, A

laska

61

:11

N14

.9°F

Bir

min

gh

am

, A

lab

am

a3

3:3

2 N

41.

7°F

Ch

arl

esto

n,

So

uth

Ca

rolin

a3

2:4

7 N

47.

1°F

Ch

ica

go,

Illin

ois

41

:50

N2

1.0

°F

Co

lum

bu

s,

Oh

io3

9:5

9 N

26

.3°F

Du

luth

, M

inn

eso

ta4

6:4

7 N

7.0

°F

Fa

irb

an

ks, A

laska

64

:50

N-

10

.1°F

Ga

lve

sto

n, Texa

s2

9:1

4 N

52

.9°F

Ho

no

lulu

, H

aw

aii

21

:19

N7

2.9

°F

La

s V

ega

s,

Neva

da

36

:12

N4

5.1

°F

Mia

mi, F

lori

da

25

:47

N6

7.3

°F

Ric

hm

on

d, V

irg

inia

37

:32

N3

5.8

°F

Tu

cso

n, A

rizo

na

32

:12

N5

1.3

°F

4-5

024_

035_

ALG

1_A

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04_C

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6049

9.in

dd

3512

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7 A

M



Co

pyr

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© G

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McG

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mp

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PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

36

Gle

ncoe

Alg

ebra

1

Exer

cise

sT

he

tab

le s

how

s th

e n

um

ber

of

mil

lion

s of

dol

lars

of

dir

ect

pol

itic

al c

ontr

ibu

tion

s re

ceiv

ed b

y D

emoc

rats

an

d R

epu

bli

can

sin

sel

ecte

d y

ears

.1.

Use

a s

prea

dsh

eet

to d

raw

a s

catt

er p

lot

and

a tr

endl

ine

for

the

data

. Let

x r

epre

sen

t th

e n

um

ber

of y

ears

sin

ce 1

990

and

let

y re

pres

ent

dire

ct p

olit

ical

con

trib

uti

ons

in m

illi

ons

of d

olla

rs.

See

stu

den

ts’ w

ork

.

2. P

redi

ct t

he

amou

nt

of d

irec

t po

liti

cal

con

trib

uti

ons

for

the

2010

ele

ctio

n.

Sam

ple

an

swer

: $1

169

mill

ion

or

$1.1

69 b

illio

n

Spre

adsh

eet

Act

ivit

yS

catt

er

Plo

ts

T

he

tab

le b

elow

sh

ows

the

nu

mb

er o

f m

etri

c to

ns

of g

old

pro

du

ced

in

min

es i

n t

he

Un

ited

Sta

tes

in s

elec

ted

yea

rs.

Use

a s

pre

adsh

eet

to d

raw

a s

catt

er p

lot

and

a t

ren

dli

ne

for

the

dat

a.

Let

x r

epre

sen

t th

e n

um

ber

of

year

s si

nce

200

0 an

d l

et y

rep

rese

nt

the

nu

mb

er o

f m

etri

c to

ns

of g

old

. Th

en p

red

ict

the

nu

mb

er o

f ou

nce

s of

go

ld p

rod

uce

d i

n 2

013.

Ste

p 1

U

se C

olu

mn

A f

or t

he

year

s si

nce

200

0 an

d C

olu

mn

B f

or t

he

nu

mbe

r of

met

ric

ton

s of

gol

d. T

o cr

eate

a g

raph

fro

m t

he

data

, sel

ect

the

data

in

Col

um

ns

A a

nd

B

and

choo

se C

har

t fr

om t

he

Inse

rt m

enu

. Sel

ect

an X

Y (

Sca

tter

) ch

art

to s

how

th

e da

ta p

oin

ts.

Ste

p 2

A

dd a

tre

ndl

ine

to t

he

grap

h b

y ch

oosi

ng

the

Ch

art

men

u. A

dd a

lin

ear

tren

dlin

e. U

se t

he

opti

ons

men

u t

o h

ave

the

tren

dlin

e fo

reca

st 5

yea

rs f

orw

ard.

U

sing

thi

s tr

endl

ine,

it

appe

ars

that

the

gol

d pr

oduc

tion

for

201

3 w

ill

be

appr

oxim

atel

y 15

0 m

etri

c to

ns.

A s

prea

dsh

eet

prog

ram

can

cre

ate

scat

ter

plot

s of

dat

a th

at y

ou e

nte

r. Yo

u c

an a

lso

hav

e th

e sp

read

shee

t gr

aph

a l

ine

of f

it, c

alle

d a

tren

dli

ne,

au

tom

atic

ally

.

Exam

ple

Sour

ce: O

pen

Secr

ets

Year

Co

ntr

ibu

tio

ns

19

90

28

1

19

94

33

7

19

98

44

5

20

02

717

20

06

10

85

Sour

ce: U

.S. G

eolo

gica

l Sur

vey

Yea

r 2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

Go

ld

353

335

298

277

247

256

252

238

233

210

4-5

A1

0 1 2 3 4 5 6 7 8 9

353

335

298

277

247

256

252

238

233

210

3 4 5 6 7 8 9 10 11 12 13 142

BC

DE

FG

H

15Sp

read

shee

t sa

mp

le

Sh

eet

1S

hee

t 2

Sh

eet

3

U.S.

Gol

d M

ine

Prod

uctio

n

Gold (metric tons)

100

150 50 0

200

250

300

350

400

Year

s si

nce

2000

510

15

036_

048_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

3612

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10

12:4

7 A

M


NA

ME

DAT

E

P

ER

IOD

Lesson 4-6

Cha

pte

r 4

37

Gle

ncoe

Alg

ebra

1

Equ

atio

ns

of

Bes

t-Fi

t Li

nes

Man

y gr

aph

ing

calc

ula

tors

uti

lize

an

alg

orit

hm

cal

led

lin

ear

regr

essi

on t

o fi

nd

a pr

ecis

e li

ne

of f

it c

alle

d th

e b

est-

fit

lin

e. T

he

calc

ula

tor

com

pute

s th

e da

ta, w

rite

s an

equ

atio

n, a

nd

give

s yo

u t

he

corr

elat

ion

coe

ffic

ent,

a

mea

sure

of

how

clo

sely

th

e eq

uat

ion

mod

els

the

data

.

GA

S PR

ICES

Th

e ta

ble

sh

ows

the

pri

ce o

f a

gall

on o

f re

gula

r ga

soli

ne

at a

sta

tion

in

Los

An

gele

s, C

alif

orn

ia o

n J

anu

ary

1 of

var

iou

s ye

ars.

Year

20

05

20

06

20

07

20

08

20

09

2010

Ave

rag

e P

rice

$1.

47

$1.

82

$2

.15

$2

.49

$2

.83

$3

.04

Sour

ce: U

.S. D

epar

tmen

t of

Ene

rgy

a. U

se a

gra

ph

ing

calc

ula

tor

to w

rite

an

eq

uat

ion

for

th

e b

est-

fit

lin

e fo

r th

at d

ata.

En

ter

the

data

by

pres

sin

g S

TA

T

and

sele

ctin

g th

e E

dit

opti

on. L

et t

he

year

200

5 be

rep

rese

nte

d by

0. E

nte

r th

e ye

ars

sin

ce 2

005

into

Lis

t 1

(L1)

. En

ter

the

aver

age

pric

e in

to L

ist

2 (L

2).

Th

en, p

erfo

rm t

he

lin

ear

regr

essi

on b

y pr

essi

ng

ST

AT

an

d se

lect

ing

the

CA

LC

opt

ion

. Scr

oll

dow

n t

o L

inR

eg (

ax+

b) a

nd

pres

s E

NT

ER

. Th

e be

st-f

it e

quat

ion

for

th

e re

gres

sion

is

show

n

to b

e y

= 0

.321

x +

1.4

99.

b.

Nam

e th

e co

rrel

atio

n c

oeff

icie

nt.

Th

e co

rrel

atio

n c

oeff

icie

nt

is t

he

valu

e sh

own

for

r o

n t

he

calc

ula

tor

scre

en. T

he

corr

elat

ion

co

effi

cien

t is

abo

ut

0.99

8.

Exer

cise

sW

rite

an

eq

uat

ion

of

the

regr

essi

on l

ine

for

the

dat

a in

eac

h t

able

bel

ow. T

hen

fi

nd

th

e co

rrel

atio

n c

oeff

icie

nt.

1. O

LYM

PIC

S B

elow

is

a ta

ble

show

ing

the

nu

mbe

r of

gol

d m

edal

s w

on b

y th

e U

nit

ed

Sta

tes

at t

he

Win

ter

Oly

mpi

cs d

uri

ng

vari

ous

year

s.Ye

ar19

92

19

94

19

98

20

02

20

06

2010

Go

ld M

edal

s5

66

10

99

Sour

ce: I

nter

natio

nal O

lym

pic

Com

mitt

ee

L

et x

rep

rese

nt

year

s si

nce

199

2; y

= 0.

25x +

5.4

1; r

= 0

.843

2. I

NTE

RES

T R

ATE

S B

elow

is

a ta

ble

show

ing

the

U.S

. Fed

eral

Res

erve

’s p

rim

e in

tere

st

rate

on

Jan

uar

y 1

of v

ario

us

year

s.Ye

ar2

00

62

00

72

00

82

00

92

010

Pri

me

Rat

e (p

erce

nt)

7.2

58

.25

7.2

53

.25

3.2

5

Sour

ce: F

eder

al R

eser

ve B

oard

L

et x

rep

rese

nt

year

s si

nce

20

06;

y =

-

1.3x

+ 8

.45;

r =

-0.

853

Stud

y G

uide

and

Inte

rven

tion

Reg

ressio

n a

nd

Med

ian

-Fit

Lin

es

Exam

ple

4-6

036_

048_

ALG

1_A

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M_C

04_C

R_6

6049

9.in

dd

3712

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10

12:4

7 A

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

38

Gle

ncoe

Alg

ebra

1

Equ

atio

ns

of

Med

ian

-Fit

Lin

es A

gra

phin

g ca

lcu

lato

r ca

n a

lso

fin

d an

oth

er t

ype

of

best

-fit

lin

e ca

lled

th

e m

edia

n-f

it l

ine,

wh

ich

is

fou

nd

usi

ng

the

med

ian

s of

th

e co

ordi

nat

es

of t

he

data

poi

nts

. ELEC

TIO

NS

Th

e ta

ble

sh

ows

the

tota

l n

um

ber

of

peo

ple

in

mil

lion

s w

ho

vote

d i

n t

he

U.S

. Pre

sid

enti

al e

lect

ion

in

th

e gi

ven

yea

rs.

Year

19

80

19

84

19

88

19

92

19

96

20

04

2

00

8

Vote

rs8

6.5

92

.79

1.6

10

4.4

96

.312

2.3

13

1.3

Sour

ce: G

eorg

e M

ason

Uni

vers

ity

a. F

ind

an

eq

uat

ion

for

th

e m

edia

n-f

it l

ine.

En

ter

the

data

by

pres

sin

g S

TA

T a

nd

sele

ctin

g th

e E

dit

opti

on. L

et t

he

year

198

0 be

rep

rese

nte

d by

0. E

nte

r th

e ye

ars

sin

ce 1

980

into

Lis

t 1

(L1)

. E

nte

r th

e n

um

ber

of v

oter

s in

to L

ist

2 (L

2).

Th

en, p

ress

S

TA

T a

nd

sele

ct t

he

CA

LC

opt

ion

. Scr

oll

dow

n t

o M

ed-M

ed o

ptio

n a

nd

pres

s E

NT

ER

. Th

e va

lue

of a

is

the

slop

e,

and

the

valu

e of

b i

s th

e y-

inte

rcep

t.T

he

equ

atio

n f

or t

he

med

ian

-fit

lin

e is

y =

1.5

5x +

8

3.5

7.

b.

Est

imat

e th

e n

um

ber

of

peo

ple

wh

o vo

ted

in

th

e 20

00 U

.S.

Pre

sid

enti

al e

lect

ion

. Gra

ph t

he

best

-fit

lin

e. T

hen

use

th

e T

RA

CE

feat

ure

an

d th

e ar

row

key

s u

nti

l yo

u f

ind

a po

int

wh

ere

x =

20.

Wh

en x

= 2

0, y

≈ 1

15. T

her

efor

e, a

bou

t 11

5 m

illi

on p

eopl

e vo

ted

in t

he

2000

U.S

. P

resi

den

tial

ele

ctio

n.

Exer

cise

sW

rite

an

eq

uat

ion

of

the

regr

essi

on l

ine

for

the

dat

a in

eac

h t

able

bel

ow. T

hen

fi

nd

th

e co

rrel

atio

n c

oeff

icie

nt.

1. P

OPU

LATI

ON

GR

OW

TH B

elow

is

a ta

ble

show

ing

the

esti

mat

ed p

opu

lati

on o

f Ari

zon

a in

mil

lion

s on

Ju

ly 1

st o

f va

riou

s ye

ars.

Year

20

01

20

02

20

03

20

04

20

05

20

06

Po

pu

lati

on

5.3

05

.44

5.5

85

.74

5.9

46

.17

Sour

ce: U

.S. C

ensu

s B

urea

u

a. F

ind

an e

quat

ion

for

th

e m

edia

n-f

it l

ine.

y =

0.1

71x +

5.2

67b

. P

redi

ct t

he

popu

lati

on o

f Ari

zon

a in

200

9. a

bo

ut

6.63

mill

ion

2. E

NR

OLL

MEN

T B

elow

is

a ta

ble

show

ing

the

nu

mbe

r of

stu

den

ts e

nro

lled

at

Hap

py

Day

s P

resc

hoo

l in

th

e gi

ven

yea

rs.

Year

20

02

20

04

20

06

20

08

2010

Stu

den

ts13

016

818

42

01

23

4

a. F

ind

an e

quat

ion

for

th

e m

edia

n-f

it l

ine.

y =

11.

42x +

137

.83

b.

Est

imat

e h

ow m

any

stu

den

ts w

ere

enro

lled

in

200

7. a

bo

ut

195

stu

den

ts

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Reg

ressio

n a

nd

Med

ian

-Fit

Lin

es

Exam

ple

4-6

036_

048_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

3812

/21/

10

12:4

7 A

M


NA

ME

DAT

E

P

ER

IOD

Lesson 4-6

Cha

pte

r 4

39

Gle

ncoe

Alg

ebra

1

Wri

te a

n e

qu

atio

n o

f th

e re

gres

sion

lin

e fo

r th

e d

ata

in e

ach

tab

le b

elow

. Th

en

fin

d t

he

corr

elat

ion

coe

ffic

ien

t.

1. S

OC

CER

Th

e ta

ble

show

s th

e n

um

ber

of g

oals

a s

occe

r te

am s

core

d ea

ch s

easo

n

sin

ce 2

005.

y =

1.

31x +

44.

38;

r =

0.7

14Ye

ar2

00

52

00

62

00

72

00

82

00

92

010

Go

als

Sco

red

42

48

46

50

52

48

2. P

HY

SIC

AL

FITN

ESS

Th

e ta

ble

show

s th

e pe

rcen

tage

of

seve

nth

gra

de s

tude

nts

in

pu

blic

sch

ool

wh

o m

et a

ll s

ix o

f C

alif

orn

ia’s

ph

ysic

al f

itn

ess

stan

dard

s ea

ch y

ear

sin

ce 2

002.

y =

3.1

4x +

29.

06;

r =

0.7

59Ye

ar2

00

22

00

32

00

42

00

52

00

6

Per

cen

tag

e2

4.0

%3

6.4

%3

8.0

%4

0.8

%3

7.5

%

Sour

ce: C

alifo

rnia

Dep

artm

ent

of E

duca

tion

3. T

AX

ES T

he

tabl

e sh

ows

the

esti

mat

ed s

ales

tax

rev

enu

es, i

n b

illi

ons

of d

olla

rs, f

or

Mas

sach

use

tts

each

yea

r si

nce

200

4. y

= 0.

172x

+ 3

.712

; r

= 0

.979

Year

20

04

20

05

20

06

20

07

20

08

Tax

Rev

enu

e3

.75

3.8

94

.00

4.1

74

.47

Sour

ce: B

eaco

n H

ill In

stitu

te

4. P

UR

CH

ASI

NG

Th

e S

ure

Sav

e su

perm

arke

t ch

ain

clo

sely

mon

itor

s h

ow m

any

diap

ers

are

sold

eac

h y

ear

so t

hat

th

ey c

an r

easo

nab

ly p

redi

ct h

ow m

any

diap

ers

wil

l be

sol

d in

th

e fo

llow

ing

year

.

Year

20

06

20

07

20

08

20

09

2010

Dia

per

s S

old

60

,20

06

5,0

00

66

,30

06

5,2

00

70

,60

0

a. F

ind

an e

quat

ion

for

th

e m

edia

n-f

it l

ine.

y =

17

67x +

62,

067

b.

How

man

y di

aper

s sh

ould

Su

reS

ave

anti

cipa

te s

elli

ng

in 2

011?

ab

ou

t 70

,90

0

5. F

AR

MIN

G S

ome

crop

s, s

uch

as

barl

ey, a

re v

ery

sen

siti

ve t

o h

ow a

cidi

c th

e so

il i

s. T

o de

term

ine

the

idea

l le

vel

of a

cidi

ty, a

far

mer

mea

sure

d h

ow m

any

bush

els

of b

arle

y h

e h

arve

sts

in d

iffe

ren

t fi

elds

wit

h v

aryi

ng

acid

ity

leve

ls.

So

il A

cid

ity

(pH

)5

.76

.26

.66

.87.

1

Bu

shel

s H

arve

sted

32

04

86

17

3

a. F

ind

an e

quat

ion

for

th

e re

gres

sion

lin

e. y

= 5

2.7x

- 3

00;

r =

0.9

91

b.

Acc

ordi

ng

to t

he

equ

atio

n, h

ow m

any

bush

els

wou

ld t

he

farm

er h

arve

st i

f th

e so

il h

ad

a pH

of

10?

abo

ut

227

bush

els

c. I

s th

is a

rea

son

able

pre

dict

ion

? E

xpla

in.

No

, bec

ause

bar

ley

may

no

t g

row

w

ell a

t ve

ry la

rge

pH

val

ues

.

Skill

s Pr

acti

ceR

eg

ressio

n a

nd

Med

ian

-Fit

Lin

es

4-6

036_

048_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

3912

/21/

10

12:4

7 A

M



Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF 2nd



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

40

Gle

ncoe

Alg

ebra

1

Wri

te a

n e

qu

atio

n o

f th

e re

gres

sion

lin

e fo

r th

e d

ata

in e

ach

tab

le b

elow

. Th

en

fin

d t

he

corr

elat

ion

coe

ffic

ien

t.

1. T

UR

TLES

Th

e ta

ble

show

s th

e n

um

ber

of t

urt

les

hat

ched

at

a zo

o ea

ch y

ear

sin

ce 2

006.

Year

20

06

20

07

20

08

20

09

2010

Turt

les

Hat

ched

21

17

16

16

14

y

= –1.

5x +

19.

8; r

= -

0.91

6

2. S

CH

OO

L LU

NC

HES

Th

e ta

ble

show

s th

e pe

rcen

tage

of

stu

den

ts r

ecei

vin

g fr

ee o

r re

duce

d pr

ice

sch

ool

lun

ches

at

a ce

rtai

n s

choo

l ea

ch y

ear

sin

ce 2

006.

Year

20

06

20

07

20

08

20

09

2010

Per

cen

tag

e14

.4%

15

.8%

18

.3%

18

.6%

20

.9%

So

urce

: Kid

sDat

a

y

= 1.

58x +

14.

44;

r =

0.9

83

3. S

POR

TS B

elow

is

a ta

ble

show

ing

the

nu

mbe

r of

stu

den

ts s

ign

ed u

p to

pla

y la

cros

se

afte

r sc

hoo

l in

eac

h a

ge g

rou

p.

Ag

e13

14

15

16

17

Lac

ross

e P

laye

rs17

14

69

12

4. L

AN

GU

AG

E T

he

Sta

te o

f C

alif

orn

ia k

eeps

tra

ck o

f h

ow m

any

mil

lion

s of

stu

den

ts a

re

lear

nin

g E

ngl

ish

as

a se

con

d la

ngu

age

each

yea

r.

Year

20

03

20

04

20

05

20

06

20

07

En

glis

h L

earn

ers

1.6

00

1.5

99

1.5

92

1.5

70

1.5

69

Sour

ce: C

alifo

rnia

Dep

artm

ent

of E

duca

tion

a. F

ind

an e

quat

ion

for

th

e m

edia

n-f

it l

ine.

y =

-

0.01

x +

1.6

07

b.

Pre

dict

th

e n

um

ber

of s

tude

nts

wh

o w

ere

lear

nin

g E

ngl

ish

in

Cal

ifor

nia

in

200

1.

ab

ou

t 1,

627,

00

0 st

ud

ents

c. P

redi

ct t

he

nu

mbe

r of

stu

den

ts w

ho

wer

e le

arn

ing

En

glis

h i

n C

alif

orn

ia i

n 2

010.

abo

ut

1,53

7,0

00

stu

den

ts

5. P

OPU

LATI

ON

Det

roit

, Mic

hig

an, l

ike

a n

um

ber

of l

arge

cit

ies,

is

losi

ng

popu

lati

on

ever

y ye

ar. B

elow

is

a ta

ble

show

ing

the

popu

lati

on o

f D

etro

it e

ach

dec

ade.

Year

19

60

19

70

19

80

19

90

20

00

Po

pu

lati

on

(m

illio

ns)

1.6

71.

51

1.2

01.

03

0.9

5

Sour

ce: U

.S. C

ensu

s B

urea

u

a. F

ind

an e

quat

ion

for

th

e re

gres

sion

lin

e. y

= -

0.01

9x +

1.6

56

b.

Fin

d th

e co

rrel

atio

n c

oeff

icie

nt

and

expl

ain

th

e m

ean

ing

of i

ts s

ign

.r

= -

0.98

2; T

he

sig

n is

neg

ativ

e, m

ean

ing

th

at t

her

e is

a n

egat

ive

corr

elat

ion

to

th

e d

ata.

c. E

stim

ate

the

popu

lati

on o

f D

etro

it i

n 2

008.

ab

ou

t 73

4,0

00

peo

ple

Prac

tice

Reg

ressio

n a

nd

Med

ian

-Fit

Lin

es

y =

-

1.5x

+ 3

4.1;

r =

-0.

554

4-6

036_

048_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

4012

/23/

10

12:3

4 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 4-6

4-6

Cha

pte

r 4

41

Gle

ncoe

Alg

ebra

1

Wor

d Pr

oble

m P

ract

ice

Reg

ressio

n a

nd

Med

ian

-Fit

Lin

es

1. F

OO

TBA

LL R

utg

ers

Un

iver

sity

ru

nn

ing

back

Ray

Ric

e ra

n f

or 1

732

tota

l ya

rds

in

the

2007

reg

ula

r se

ason

. Th

e ta

ble

belo

w

show

s h

is c

um

ula

tive

tot

al n

um

ber

of

yard

s ra

n a

fter

sel

ect

gam

es.

Gam

e N

um

ber

13

69

12

Cu

mu

lati

ve

Yard

s18

44

31

818

12

57

17

32

Sour

ce: R

utge

rs U

nive

rsity

Ath

letic

s

U

se a

cal

cula

tor

to f

ind

an e

quat

ion

for

th

e re

gres

sion

lin

e sh

owin

g th

e to

tal

yard

s y

scor

ed a

fter

x g

ames

. Wh

at i

s th

e re

al-w

orld

mea

nin

g of

th

e va

lue

retu

rned

for

a?

y

= 14

0.4x

+ 1

3.8;

a r

epre

sen

ts

the

nu

mb

er o

f ya

rds

Ray

Ric

e ca

n

be

exp

ecte

d t

o r

un

per

gam

e.

2. G

OLD

Ou

nce

s of

gol

d ar

e tr

aded

by

larg

e in

vest

men

t ba

nks

in

com

mod

ity

exch

ange

s m

uch

th

e sa

me

way

th

at

shar

es o

f st

ock

are

trad

ed. T

he

tabl

e be

low

sh

ows

the

cost

of

a si

ngl

e ou

nce

of

gold

on

th

e la

st d

ay o

f tr

adin

g in

giv

en

year

s.

Year

2002

2003

2004

2005

2006

Pri

ce

$346.7

0$414.8

0$438.1

0$517.

20

$636.3

0

Sour

ce: G

loba

l Fin

anci

al D

ata

U

se a

cal

cula

tor

to f

ind

an e

quat

ion

for

th

e re

gres

sion

lin

e. T

hen

pre

dict

th

e pr

ice

of a

n o

un

ce o

f go

ld o

n t

he

last

day

of

tra

din

g in

200

9. I

s th

is a

rea

son

able

pr

edic

tion

? E

xpla

in.

y

= 68

.16x

+ 3

34.3

; $8

11.4

2; T

he

pre

dic

tio

n m

ay n

ot

be

reas

on

able

, b

ecau

se t

he

valu

e o

f an

in

vest

men

t ca

n fl

uct

uat

e.

3. G

OLF

SC

OR

ES E

mm

anu

el i

s pr

acti

cin

g go

lf a

s pa

rt o

f h

is s

choo

l’s g

olf

team

. E

ach

wee

k h

e pl

ays

a fu

ll r

oun

d of

gol

f an

d re

cord

s h

is t

otal

sco

re. H

is s

core

card

af

ter

five

wee

ks i

s be

low

.W

eek

12

34

5

Go

lf S

core

112

10

710

810

49

8

U

se a

cal

cula

tor

to f

ind

an e

quat

ion

for

th

e m

edia

n-f

it l

ine.

Th

en e

stim

ate

how

m

any

gam

es E

mm

anu

el w

ill

hav

e to

pla

y to

get

a s

core

of

86.

y

= -

2.83

x +

114

.67;

ab

ou

t 10

g

ames

4. S

TUD

ENT

ELEC

TIO

NS

Th

e vo

te t

otal

s fo

r fi

ve o

f th

e ca

ndi

date

s pa

rtic

ipat

ing

in

Mon

tval

e H

igh

Sch

ool’s

stu

den

t co

un

cil

elec

tion

s an

d th

e n

um

ber

of h

ours

eac

h

can

dida

te s

pen

t ca

mpa

ign

ing

are

show

n

in t

he

tabl

e be

low

.

Ho

urs

C

amp

aig

nin

g1

34

68

Vote

s R

ecei

ved

92

22

44

67

8

a. U

se a

cal

cula

tor

to f

ind

an e

quat

ion

fo

r th

e m

edia

n-f

it l

ine.

y =

9.

3x -

6.4

7

b.

Plo

t th

e da

ta p

oin

ts a

nd

draw

th

e m

edia

n-f

it l

ine

on t

he

grap

h b

elow

.

Votes Received

2030 10 04050607080

Cam

paig

n Ti

me

(h)

32

15

74

68

x

y

c. S

upp

ose

a si

xth

can

dida

te s

pen

ds

7 h

ours

cam

paig

nin

g. E

stim

ate

how

m

any

vote

s th

at c

andi

date

cou

ld

expe

ct t

o re

ceiv

e. a

bo

ut

59

4-6

036_

048_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

4112

/23/

10

2:30

PM



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

42

Gle

ncoe

Alg

ebra

1

For

som

e se

ts o

f da

ta, a

lin

ear

equ

atio

n i

n t

he

form

y =

ax

+ b

doe

s n

ot a

dequ

atel

y de

scri

be

the

rela

tion

ship

bet

wee

n d

ata

poin

ts. T

he

“Qu

adR

eg”

fun

ctio

n o

n a

gra

phin

g ca

lcu

lato

r w

ill

outp

ut

an e

quat

ion

in

th

e fo

rm y

= a

x2 +

bx

+ c

. Th

e va

lue

of R

2 , th

e co

effi

cien

t of

d

eter

min

atio

n t

ells

you

how

clo

sely

th

e pa

rabo

la f

its

the

data

.

T

he

tab

le s

how

s th

e p

opu

lati

on o

f A

tlan

ta i

n v

ario

us

year

s.

Year

19

70

19

80

19

90

20

00

20

05

20

07

Po

pu

lati

on

49

7,0

00

42

5,0

00

39

4,0

17

416

,474

47

0,6

88

49

8,1

09

Sour

ce: U

.S. C

ensu

s B

urea

u

a. F

ind

th

e eq

uat

ion

of

a q

uad

rati

c-re

gres

sion

par

abol

a fo

r th

e d

ata.

Ru

nn

ing

a li

nea

r re

gres

sion

on

th

e da

ta p

rovi

des

an r

val

ue

of 0

.03,

wh

ich

in

dica

tes

a po

or f

it. T

he

data

app

ears

to

be a

goo

d ca

ndi

date

for

a q

uad

rati

c re

gres

sion

.

Ste

p 1

E

nte

r th

e da

ta b

y pr

essi

ng

ST

AT

an

d se

lect

ing

the

Edi

t op

tion

. En

ter

the

year

s si

nce

197

0 as

you

r x-

valu

es (

L1)

an

d en

ter

the

popu

lati

on f

igu

res

as y

our

y-va

lues

(L

2).

Ste

p 2

P

erfo

rm t

he

quad

rati

c re

gres

sion

by

pres

sin

g S

TA

T a

nd

sele

ctin

g th

e C

AL

C o

ptio

n. S

crol

l do

wn

to

Qu

adR

eg a

nd

pres

s E

NT

ER

.

Ste

p 3

W

rite

th

e eq

uat

ion

of

the

best

-fit

par

abol

a by

rou

ndi

ng

the

a, b

, an

d c

valu

es o

n t

he

scre

en.

Th

e eq

uat

ion

for

th

e be

st-f

it p

arab

ola

is

y=

302

.8x2

– 1

1,48

0x +

501

,227

.b

. F

ind

th

e co

effi

cien

t of

det

erm

inat

ion

.

Th

e co

effi

cien

t of

det

erm

inat

ion

for

th

e pa

rabo

la i

s R

2 =

0.9

69,

wh

ich

in

dica

tes

a go

od f

it.

c. U

se t

he

qu

adra

tic-

regr

essi

on p

arab

ola

to p

red

ict

the

pop

ula

tion

in

201

0.

Gra

ph t

he

best

-fit

par

abol

a. T

hen

use

th

e T

RA

CE

fea

ture

an

d th

e ar

row

key

s u

nti

l yo

u f

ind

a po

int

wh

ere

x =

40.

Whe

n x

≈ 40

, y ≈

52

5,00

0. T

he e

stim

ated

pop

ulat

ion

wil

l be

525,

000.

Exer

cise

s

1. T

he

tabl

e be

low

sh

ows

the

aver

age

hig

h t

empe

ratu

re i

n C

ryst

al

Riv

er, F

lori

da i

n v

ario

us

mon

ths.

Mo

nth

Ja

n (

1)

Ma

r (3

)M

ay (

5)

Jul (7

)S

ep

(9

)N

ov (

11)

Avg

. Hig

h (

°F)

68

°76

°8

7°

91

°8

8°

76

°

Sour

ce: C

ount

ry S

tudi

es

a. F

ind

the

equ

atio

n o

f th

e be

st-f

it p

arab

ola.

y =

-0.

696x

2 +

9.5

x +

57.

20

b.

Fin

d th

e co

effi

cien

t of

det

erm

inat

ion

. R

2 =

0.

943

c. U

se t

he

quad

rati

c-re

gres

sion

par

abol

a to

pre

dict

th

e av

erag

e h

igh

tem

pera

ture

in

A

pril

(4t

h m

onth

).

Enri

chm

ent

Qu

ad

rati

c R

eg

ressio

n P

ara

bo

las

Exam

ple

abo

ut

84°F

4-6

036_

048_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

4212

/21/

10

12:4

7 A

M



NA

ME

DAT

E

P

ER

IOD

Lesson 4-7

Cha

pte

r 4

43

Gle

ncoe

Alg

ebra

1

Inve

rse

Rel

atio

ns

An

in

vers

e re

lati

on i

s th

e se

t of

ord

ered

pai

rs o

btai

ned

by

exch

angi

ng

the

x-co

ordi

nat

es w

ith

th

e y-

coor

din

ates

of

each

ord

ered

pai

r. T

he

dom

ain

of

a re

lati

on b

ecom

es t

he

ran

ge o

f it

s in

vers

e, a

nd

the

ran

ge o

f th

e re

lati

on b

ecom

es t

he

dom

ain

of

its

in

vers

e.

F

ind

an

d g

rap

h t

he

inve

rse

of t

he

rela

tion

rep

rese

nte

d b

y li

ne

a.

Th

e gr

aph

of

the

rela

tion

pas

ses

thro

ugh

(–2,

–10

), (–

1, –

7), (

0, –

4), (

1, –

1), (

2, 2

), (3

, 5),

and

(4, 8

).

To

fin

d th

e in

vers

e, e

xch

ange

th

e co

ordi

nat

es

of t

he

orde

red

pair

s.

Th

e gr

aph

of

the

inve

rse

pass

es t

hro

ugh

th

e po

ints

(–

10, –

2), (

–7,

–1)

, (–4,

0),

(–1,

1),

(2, 2

), (5

, 3),

and

(8, 4

). G

raph

th

ese

poin

ts a

nd

then

dra

w t

he

lin

e th

at p

asse

s th

rou

gh t

hem

.

Exer

cise

sF

ind

th

e in

vers

e of

eac

h r

elat

ion

.

1. {

(4, 7

), (6

, 2),

(9, –

1), (

11, 3

)}

2. {

(–5,

–9)

, (–4,

–6)

, (–2,

–4)

, (0,

–3)

}

3.

xy

–8

–15

–2

–11

1–

8

51

118

4.

x

y

–8

3

–2

9

213

618

819

5.

x

y

–6

14

–5

11

–4

8

–3

5

–2

2

Gra

ph

th

e in

vers

e of

eac

h r

elat

ion

.

6.

y

xO8 4

−4

−8

48

−4

−8

7.

y

xO8 4

−4

−8

48

−4

−8

8.

y

xO8 4

−4

−8

48

−4

−8

Stud

y G

uide

Invers

e L

inear

Fu

ncti

on

s

Exam

ple

{(7,

4),

(2, 6

), (-

1, 9

), (3

, 11)

}

{(-

15, -

8), (

-11

, -2)

, ( -

8, 1

), (1

, 5),

(8, 1

1)}

{(3,

-8)

, (9,

-2)

, (1

3, 2

), (1

8, 6

), (1

9, 8

)}{(

14, -

6), (

11, -

5),

(8, -

4), (

5, -

3), (

2, -

2)}

{(-

9, -

5), (

-6,

-4)

, (-

4, -

2), (

-3,

0)}

y

xO8 4

−4

−8

48

−4

−8

( −10

, −2)

( −4,

0)

( 2, 2

)( 8, 4

)

a

4-7

036_

048_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

4312

/21/

10

12:4

7 A

M


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass




NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

44

Gle

ncoe

Alg

ebra

1

Stud

y G

uide

(co

nti

nu

ed)

Invers

e L

inear

Fu

ncti

on

s

Inve

rse

Fun

ctio

ns

A l

inea

r re

lati

on t

hat

is

desc

ribe

d by

a f

un

ctio

n h

as a

n i

nve

rse

fun

ctio

n t

hat

can

gen

erat

e or

dere

d pa

irs

of t

he

inve

rse

rela

tion

. Th

e in

vers

e of

th

e li

nea

r fu

nct

ion

f (x

) ca

n b

e w

ritt

en a

s f -

1 (x)

an

d is

rea

d f

of x

in

vers

e or

th

e in

vers

e of

f o

f x.

F

ind

th

e in

vers

e of

f (x

) =

3 −

4 x +

6.

Ste

p 1

f (x

) =

3 −

4 x +

6

Ori

gin

al equation

y

= 3 −

4 x +

6

Repla

ce f

(x)

with y

.

Ste

p 2

x =

3 −

4 y +

6

Inte

rchange y

and x

.

Ste

p 3

x

- 6

= 3 −

4 y

Subtr

act

6 f

rom

each s

ide.

4 −

3 (x -

6)

= y

M

ultip

ly e

ach s

ide b

y 4

−

3 .

Ste

p 4

4 −

3 (x -

6) =

f -

1 (x)

R

epla

ce y

with f

-1 (x

).

Th

e in

vers

e of

f (x

) =

3 −

4 x +

6 i

s f -

1 (x)

= 4 −

3 (x -

6)

or f

-1 (

x) =

4 −

3 x -

8.

Exer

cise

sF

ind

th

e in

vers

e of

eac

h f

un

ctio

n.

1.

f (x)

= 4

x -

3

2.

f (x)

= -

3x +

7

3.

f (x)

= 3 −

2 x -

8

f

-1 (

x)

= x

+ 3

−

4

f -

1 (x)

= 7

- x

−

3

f -

1 (x)

= 2 −

3 x +

16

−

3

4.

f (x)

= 1

6 -

1 −

3 x

5.

f (x)

= 3

(x -

5)

6.

f (x)

= -

15 -

2 −

5 x

f

-1 (

x)

= -

3x +

48

f -

1 (x)

= x

−

3 + 5

f

-1 (

x)

= -

5 −

2 (x +

15)

7. T

OO

LS J

imm

y re

nts

a c

hai

nsa

w f

rom

th

e de

part

men

t st

ore

to w

ork

on h

is y

ard.

T

he

tota

l co

st C

(x)

in d

olla

rs i

s gi

ven

by

C(x

) =

9.9

9 +

3.0

0x, w

her

e x

is t

he

nu

mbe

r of

day

s h

e re

nts

th

e ch

ain

saw

.

a.

Fin

d th

e in

vers

e fu

nct

ion

C -

1 (x)

. C

-1 (x

) =

x -

9.9

9 −

3

b

. W

hat

do

x an

d C

-1 (

x) r

epre

sen

t in

th

e co

nte

xt o

f th

e in

vers

e fu

nct

ion

?

x re

pre

sen

ts t

he

tota

l co

st a

nd

C -

1 (x)

rep

rese

nts

th

e n

um

ber

o

f d

ays

he

ren

ts t

he

chai

nsa

w.

c.

How

man

y da

ys d

id J

imm

y re

nt

the

chai

nsa

w i

f th

e to

tal

cost

w

as $

27.9

9? 6

day

s

Exam

ple

4-7

036_

048_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

4412

/21/

10

12:4

7 A

M


NA

ME

DAT

E

P

ER

IOD

Lesson 4-7

Cha

pte

r 4

45

Gle

ncoe

Alg

ebra

1

Fin

d t

he

inve

rse

of e

ach

rel

atio

n.

1.

xy

–9

–1

–7

–4

–5

–7

–3

–10

–1

–13

2.

x

y

18

26

34

42

50

3.

x

y

–4

–2

–2

–1

01

20

42

4. {

(-3,

2),

(-1,

8),

(1, 1

4), (

3, 2

0)}

5. {

(5, -

3), (

2, -

9), (

-1,

-15

), (-

4, -

21)}

{

(2, -

3), (

8, -

1), (

14, 1

), (2

0, 3

)}

{(

-3,

5),

(-9,

2),

(-15

, -1)

, (-

21, -

4)}

6. {

(4, 6

), (3

, 1),

(2, -

4), (

1, -

9)}

7. {

(-1,

16)

, (-

2, 1

2), (

-3,

8),

(-4,

4)}

{

(6, 4

), (1

, 3),

(-4,

2),

(-9,

1)}

{(16

, -1)

, (12

, -2)

, (8,

-3)

, (4,

-4)

}

Gra

ph

th

e in

vers

e of

eac

h f

un

ctio

n.

8.

y

xO8 4

−4

−8

48

−4

−8

9.

y

xO8 4

−4

−8

48

−4

−8

10

. y

xO8 4

−4

−8

48

−4

−8

Fin

d t

he

inve

rse

of e

ach

fu

nct

ion

.

11.

f (x

) =

8x

- 5

12

. f (

x) =

6(x

+ 7

) 13

. f (

x) =

3 −

4 x +

9

f -

1 (x)

= x

+ 5

−

8

f -1 (

x)

= x

−

6 - 7

f -

1 (x)

= 4 −

3 (x -

9)

14.

f (x

) =

-16

+ 2 −

5 x

15.

f (x)

= 3x

+ 5

−

4

16.

f (x)

= -

4x +

1

−

5

f -

1 (x)

= 5 −

2 (x +

16)

f -

1 (x)

= 4x

- 5

−

3

f -1 (

x)

= 1

- 5x

−

4

17. L

EMO

NA

DE

Ch

riss

y sp

ent

$5.0

0 on

su

ppli

es a

nd

lem

onad

e po

wde

r fo

r h

er l

emon

ade

stan

d. S

he

char

ges

$0.5

0 pe

r gl

ass.

a.

Wri

te a

fu

nct

ion

P(x

) to

rep

rese

nt

her

pro

fit

per

glas

s so

ld.

P(x

) =

0.5

0x -

5.0

0

b

. F

ind

the

inve

rse

fun

ctio

n, P

-1 (

x).

P -

1 (x)

= x

+ 5

.00

−

0.50

c.

Wh

at d

o x

and

P -

1 (x)

rep

rese

nt

in t

he

con

text

of

the

inve

rse

fun

ctio

n?

x r

epre

sen

ts

the

tota

l pro

fi t a

nd

P -

1 (x)

rep

rese

nts

th

e n

um

ber

of

gla

sses

so

ld.

d

. How

man

y gl

asse

s m

ust

Ch

riss

y se

ll i

n o

rder

to

mak

e a

$3 p

rofi

t? 1

6

Skill

s Pr

acti

ceIn

vers

e L

inear

Fu

ncti

on

s

{(-

1, -

9), (

-4,

-7)

, (-

7, -

5),

(-10

, -3)

, (-

13, -

1)}

{(8,

1),

(6, 2

), (4

, 3),

(2, 4

), (0

, 5)}

{(-

2, -

4), (

-1,

-2)

, (1

, 0),

(0, 2

), (2

, 4)}

4-7

036_

048_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

4512

/21/

10

12:4

7 A

M


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF 2nd




NA

ME

DAT

E

P

ER

IOD

Lesson 4-7

Cha

pte

r 4

47

Gle

ncoe

Alg

ebra

1

Wor

d Pr

oble

m P

ract

ice

Invers

e L

inear

Fu

ncti

on

s

1. B

USI

NES

S A

lish

a st

arte

d a

baki

ng

busi

nes

s. S

he

spen

t $3

6 in

itia

lly

on

supp

lies

an

d ca

n m

ake

5 do

zen

bro

wn

ies

at a

cos

t of

$12

. Sh

e ch

arge

s h

er

cust

omer

s $1

0 pe

r do

zen

bro

wn

ies.

a.

Wri

te a

fu

nct

ion

C(x

) to

rep

rese

nt

Ali

sha’

s to

tal

cost

per

doz

en

brow

nie

s. C

(x)

=36

+ 2

.4x

b.

Wri

te a

fu

nct

ion

E(x

) to

rep

rese

nt

Ali

sha’

s ea

rnin

gs p

er d

ozen

bro

wn

ies

sold

. E

(x)

=10

x

c.

Fin

d P

(x)

=E

(x)

-C

(x).

Wh

at d

oes

P (x

) re

pres

ent?

P(x

) =

7.6

x-

36;

P

(x)

rep

rese

nts

th

e p

rofi t

th

at

Alis

ha

earn

s.

d. F

ind

C -

1 (x)

, E -

1 (x)

, an

d P

-1 (

x).

C -

1 (x)

=

x -

36

−

2.4

; E

-1 (

x)

=x

− 10;

P -

1 (x)

=

x +

36

−

7.6

e.

How

man

y do

zen

bro

wn

ies

does

A

lish

a n

eed

to s

ell

in o

rder

to

mak

e a

prof

it?

5 o

r m

ore

2. G

EOM

ETRY

Th

e ar

ea o

f th

e ba

se o

f a

cyli

ndr

ical

wat

er t

ank

is 6

6 sq

uar

e fe

et.

Th

e vo

lum

e of

wat

er i

n t

he

tan

k is

de

pen

den

t on

th

e h

eigh

t of

th

e w

ater

han

d is

rep

rese

nte

d by

th

e fu

nct

ion

V

(h)

= 6

6h. F

ind

V -

1 (h

). W

hat

wil

l th

e h

eigh

t of

th

e w

ater

be

wh

en t

he

volu

me

reac

hes

231

0 cu

bic

feet

?

V -

1 (h

) =

h− 66

; 35

fee

t

3. S

ERV

ICE

A t

ech

nic

ian

is

wor

kin

g on

a

furn

ace.

He

is p

aid

$150

per

vis

it p

lus

$70

for

ever

y h

our

he

wor

ks o

n t

he

furn

ace.

a.

Wri

te a

fu

nct

ion

C(x

) to

rep

rese

nt

the

tota

l ch

arge

for

eve

ry h

our

of

wor

k. C

(x)

= 7

0x+

150

b

. F

ind

the

inve

rse

fun

ctio

n, C

-1 (

x).

C -

1 (x)

=

x -

150

−

70

c. H

ow l

ong

did

the

tech

nic

ian

wor

k on

th

e fu

rnac

e if

th

e to

tal

char

ge w

as

$640

? 7

ho

urs

4. F

LOO

RIN

G K

ara

is h

avin

g ba

sebo

ard

inst

alle

d in

her

bas

emen

t. T

he

tota

l co

st C

(x)

in d

olla

rs i

s gi

ven

by

C(x

) =

125

+ 1

6x, w

her

e x

is t

he

nu

mbe

r of

pie

ces

of w

ood

requ

ired

fo

r th

e in

stal

lati

on.

a.

Fin

d th

e in

vers

e fu

nct

ion

C -

1 (x)

.

C -

1 (x)

=

x -

125

−

16

b.

If t

he

tota

l co

st w

as $

269

and

each

pi

ece

of w

ood

was

12

feet

lon

g, h

ow

man

y to

tal

feet

of

woo

d w

ere

use

d? 1

08 f

eet

5. B

OW

LIN

G L

ibby

’s f

amil

y w

ent

bow

lin

g du

rin

g a

hol

iday

spe

cial

. Th

e sp

ecia

l co

st

$40

for

pizz

a, b

owli

ng

shoe

s, a

nd

un

lim

ited

dri

nks

. Eac

h g

ame

cost

$2.

H

ow m

any

gam

es d

id L

ibby

bow

l if

th

e to

tal

cost

was

$11

2 an

d th

e si

x fa

mil

y m

embe

rs b

owle

d an

equ

al n

um

ber

of

gam

es?

6

4-7

036_

048_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

4712

/21/

10

12:4

7 A

M


NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

46

Gle

ncoe

Alg

ebra

1

Fin

d t

he

inve

rse

of e

ach

rel

atio

n.

1. {

(-2,

1),

(-5,

0),

(-8,

-1)

, (-

11, 2

)}

2. {

(3, 5

), (4

, 8),

(5, 1

1), (

6, 1

4)}

{

(1, -

2), (

0, -

5), (

-1,

-8)

, (2,

-11

)}

{(5,

3),

(8, 4

), (1

1, 5

), (1

4, 6

)}

3. {

(5, 1

1), (

1, 6

), (-

3, 1

), (-

7, -

4)}

4. {

(0, 3

), (2

, 3),

(4, 3

), (6

, 3)}

{

(11,

5),

(6, 1

), (1

, -3)

, (-

4, -

7)}

{(3,

0),

(3, 2

), (3

, 4),

(3, 6

)}

Gra

ph

th

e in

vers

e of

eac

h f

un

ctio

n.

5.

y

xO8 4

−4

−8

48

−4

−8

6.

y

xO8 4

−4

−8

48

−4

−8

7.

y

xO8 4

−4

−8

48

−4

−8

Fin

d t

he

inve

rse

of e

ach

fu

nct

ion

.

8.

f (x)

= 6 −

5 x -

3

9.

f (x)

= 4x

+ 2

−

3

10.

f (x)

= 3x

- 1

−

6

f -

1 (x)

= 5 −

6 (x +

3)

f -1 (

x)

= 3x

- 2

−

4

f -1 (

x)

= 6x

+ 1

−

3

11.

f (x

) =

3(3

x +

4)

12.

f (x)

= -

5(-

x -

6)

13.

f (x)

= 2x

- 3

−

7

f -

1 (x)

= x

−

3 - 4

−

3

f -1 (

x)

= x

−

5 - 6

f -

1 (x)

= 7x

+ 3

−

4

Wri

te t

he

inve

rse

of e

ach

eq

uat

ion

in

f -

1 (x)

not

atio

n.

13.

4x

+ 6

y =

24

14.

-3y

+ 5

x =

18

15.

x +

5y

= 1

2

f -

1 (x)

= 24

- 6x

−

4

f -1 (

x)

= 3x

+ 1

8 −

5

f -1 (

x)

= -

5x +

12

16.

5x

+ 8

y =

40

17.

-4y

- 3

x =

15

+ 2

y 18

. 2x

- 3

= 4

x +

5y

f -

1 (x)

= 40

- 8x

−

5

f -1 (

x)

= -

2x -

5

f -1 (

x)

= -

5x -

3

−

2

19. C

HA

RIT

Y J

enn

y is

ru

nn

ing

in a

ch

arit

y ev

ent.

On

e do

nor

is

payi

ng

an i

nit

ial

amou

nt

of

$20.

00 p

lus

an e

xtra

$5.

00 f

or e

very

mil

e th

at J

enn

y ru

ns.

a.

Wri

te a

fu

nct

ion

D(x

) fo

r th

e to

tal

don

atio

n f

or x

mil

es r

un

. D

(x)

= 5

x +

20

b

. F

ind

the

inve

rse

fun

ctio

n, D

-1 (

x).

D -

1 (x)

= x

- 2

0 −

5

c.

Wh

at d

o x

and

D -

1 (x)

rep

rese

nt

in t

he

con

text

of

the

inve

rse

fun

ctio

n?

x r

epre

sen

ts

the

tota

l do

nat

ion

an

d P

-1 (x

) re

pre

sen

ts t

he

nu

mb

er m

iles

run

.

Prac

tice

Invers

e L

inear

Fu

ncti

on

s

4-7

036_

048_

ALG

1_A

_CR

M_C

04_C

R_6

6049

9.in

dd

4612

/23/

10

12:3

8 P

M


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass




NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 4

48

Gle

ncoe

Alg

ebra

1

In a

fu

nct

ion

, th

ere

is e

xact

ly o

ne

outp

ut

for

ever

y in

put.

In

oth

er w

ords

, eve

ry e

lem

ent

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in t

he

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hen

a

fun

ctio

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s on

to, e

ach

ele

men

t of

th

e ra

nge

cor

resp

onds

to

an e

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ent

in t

he

dom

ain

.

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fu

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is

both

on

e-to

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e an

d on

to, t

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f it

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, det

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er.

1.

11 16-

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3 6 9 12

2.

1 2 3 4 5

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3.

3 6 9 12 15

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5

4.

4 2 7 11 6

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5.

2 6 13

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of e

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also

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7.

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xO8 4

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On

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On

to F

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2 6 9 12

-1 3 5 8 9

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onto

5 7 9 10

-6

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Chapter 4 Assessment Answer KeyQuiz 1 (Lessons 4-1 and 4-2) Quiz 3 (Lessons 4-5 and 4-6) Mid-Chapter TestPage 51 Page 52 Page 53

Quiz 2 (Lessons 4-3 and 4-4)

Page 51Quiz 4 (Lesson 4-7)

Page 52

1.

2.

3.

4.

5.

positive correlation; the older a person is, the higher the median income

y = 4.09x - 90.74

D

about $36,000

Age (years)

Med

ian

Inco

me

($10

00)

16

19

22

25

28

31

260 27 28 29 30

f -1 (x) = x - 6

−

4

1.

2.

3.

4.

5.

{(3, 1), (-1, 4),

(-5, 7), (-9, 10)}

f -1 (x) = 4 −

3 (x + 8)

A

y

xO

8

4

−4−8 4 8

−4

−8

1. A

2. H

3. B

4. J

5. D

6. H

7. t = 20h + 50

8.

9. $130

10. 6.5 hours

1

Hours2 3 4 5 6 7 8 9 10

20406080

100

Tota

l Cos

t ($)

120140160180200

1.

2.

3. y

xO

4.

5.

y =

1 −

4 x - 5

y = -

4 −

11 x +

58 −

11

h = 3y + 48 for h in

inches or h = 0.25y + 4

for h in feet

C

1.

2.

3.

4.

5.

y - 6 = - 1 −

3 (x - 3)

y = -x + 7

y + 1 = 0

y = -

1 −

3 x + 14

−

3

D

A25_A36_ALG1_A_CRM_C04_AN_660499.indd A25A25_A36_ALG1_A_CRM_C04_AN_660499.indd A25 12/21/10 1:24 AM12/21/10 1:24 AM

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Chapter 4 Assessment Answer KeyVocabulary Test Form 1Page 54 Page 55 Page 56

1. perpendicular lines

2. inverse relation

3. scatter plot

4. parallel lines

5. correlation coefficient

6. linear interpolation

7.

linear extrapolation

8. slope-intercept

9. point-slope

10.

Sample answer: A line of fi t

is a line that comes close to the data points for a scatter plot, even if all the data

points do not lie on that line.

11.

Sample answer: Linear

extrapolation is the process of using a linear equation to

predict a y-value for an x-value that lies beyond the extremes of the domain of

the relation.

1. C

2. H

3. D

4. F

5. A

6. H

7. C

8. H

9. B

10. G

11. BB: 7

12.

13.

14.

15.

16.

17.

18.

19.

20.

F

B

F

D

J

C

H

C

G


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Chapter 4 Assessment Answer KeyForm 2A Form 2BPage 57 Page 58 Page 59 Page 60

1. D

2. H

3. D

4. H

5. B

6. G

7. D

8. H

9. B

10. F

11. D

12. F

13. B

14. G

15. C

16. G

17. C

18. H

19. B

20. J

1. B

2. F

3. C

4. G

5. A

6. F

7. D

8. H

9. B

10. G

11. B

12. F

13. B

14. F

15. C

16. J

17. D

18. J

19. B

20. H

B: -21

B: 17

−

3


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Chapter 4 Assessment Answer KeyForm 2CPage 61 Page 62

1. y = 0.10x + 28.75

2. 5x + 7y = 14

3. y =

2 −

3 x - 2

4. y

xO

5. y =

3 −

2 x -

1 −

2

6. x = -6

7. y - 8 =

1 −

3 (x + 2)

8. 12x + 7y = -16

9. y = 3x - 10

10. y = -2x + 1

11. y =

2 −

3 x - 4

12. y = 1.25x + 2508

13.

14.

Sample answer: using

data points (20, 67) and

(40, 87), y = x + 47; 82

15.

No, because the maximum score is 100%, even for very large amounts of time studying.

16. y = 0.52x - 983.73

17. 30

18. y

xO

8

4

−4−8 4 8

−4

−8

19. f -1 (x) =

5 - 15x −

4

20. f -1 (x) =

13 - 8x −

6

B: � = 1.2t + 1.8; 6 years

Time Spent Studying(minutes)

Sco

re R

ecei

ved

(per

cen

t)

0

60

70

80

90

100

10 20 30 40 50


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Chapter 4 Assessment Answer KeyForm 2DPage 63 Page 64

1. y = 2.50x + 4.95

2. x - y = 2

3. y = -

2 −

3 x - 2

4. y

xO

5. y = -5x + 29

6. x = 5

7. y =

4 −

3 (x - 3)

8. 2x + 3y = -1

9. y =

3 −

4 x -

5 −

4

10. y = -3x + 18

11. y = -

1 −

4 x + 4

12.

13.

14.

Sample answer:

using data points (30, 6.1) and

(70, 4.7), y = -0.035x + 7.15; about 4.9

15.

No, younger people are

likely to spend a

signifi cant percentage on

entertainment because of

a lack of other expenses.

16. y = 0.25x - 467.83

17. 35

18. y

xO

8

4

−4−8 4 8

−4

−8

19. f -1 (x) =

8 - 18x −

3

20. f -1 (x) =

28 + 3x −

5

B: y =

6 −

5 x - 6

Age

Perc

ent

Spen

t o

nEn

tert

ain

men

t

3

4

5

6

300 40 50 60 70 80

y = 8.35x -

16,766.5


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Chapter 4 Assessment Answer KeyForm 3Page 65 Page 66

1. y = 3x - 8

2. y =

5 −

2 x - 11

3. y = -

3 −

5 x +

26 −

5

4. y = 6

5. y - 1= -

3 −

5 (x - 2)

6. 2x + y = 1

7.

8. 2x + 3y = 6

9. y + 2 = -

2 −

3 x

10. x = 3

11. y = -

4 −

3 x - 9

12. y =

3 −

5 x - 6

13. y = 5

y

xO

14.

15.

positive; a verbal score is closely associated with the math score

16.

Sample answer: Using

data points (424, 466) and

(460, 488); y = 0.6x + 211.6;

about 479

17.

y = -2.67x + 45.17;

about 24 seats

18. y

xO

8

4

−4−8 4 8

−4

−8

19. f -1 (x) =

12 - 8x −

15

20. f -1 (x) =

13 + 3x −

2

B: 9

Verbal Score

Mat

h S

core

450

460

470

480

490

500

4000 440 480


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Chapter 4 Assessment Answer KeyPage 67, Extended-Response Test

Scoring Rubric

Score General Description Specifi c Criteria

4 Superior

A correct solution that

is supported by well-

developed, accurate

explanations

• Shows thorough understanding of the concepts of slope, various forms of a linear equation, graphing lines from an equation, scatter plots, correlation, and predicting data.

• Uses appropriate strategies to solve problems.

• Computations are correct.

• Written explanations are exemplary.

• Graphs are accurate and appropriate.

• Goes beyond requirements of some or all problems.

3 Satisfactory

A generally correct solution,

but may contain minor fl aws

in reasoning or computation

• Shows an understanding of the concepts of slope, various forms of a linear equation, graphing lines from an equation, scatter plots, correlation, and predicting data.

• Uses appropriate strategies to solve problems.

• Computations are mostly correct.

• Written explanations are effective.

• Graphs are mostly accurate and appropriate.

• Satisfi es all requirements of problems.

2 Nearly Satisfactory

A partially correct

interpretation and/or

solution to the problem

• Shows an understanding of most of the concepts of slope, various forms of a linear equation, graphing lines from an equation, scatter plots, correlation, and predicting data.

• May not use appropriate strategies to solve problems.

• Computations are mostly correct.

• Written explanations are satisfactory.

• Graphs are mostly accurate.

• Satisfi es the requirements of most of the problems.

1 Nearly Unsatisfactory

A correct solution with no

supporting evidence or

explanation

• Final computation is correct.

• No written explanations or work is shown to substantiate

the fi nal computation.

• Graphs may be accurate but lack detail or explanation.

• Satisfi es minimal requirements of some of the problems.

0 Unsatisfactory

An incorrect solution

indicating no mathematical

understanding of the

concept or task, or no

solution is given

• Shows little or no understanding of most of the concepts of

slope, various forms of a linear equation, graphing lines from an equation, scatter plots, correlation, and predicting data.

• Does not use appropriate strategies to solve problems.

• Computations are incorrect.

• Written explanations are unsatisfactory.

• Graphs are inaccurate or inappropriate.

• Does not satisfy requirements of problems.

• No answer may be given.


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1a. In order to graph the line through (-2, 3) you need to know the slope of the line, another point on the line, or the equation of the line.

1b. If you knew the slope of the line, you could plot another point using the rise and run on a coordinate plane. If you knew another point, you could graph that point and draw a line through (-2, 3) and the other point. If you knew the equation of the line, you could use the slope-intercept form of the equation to find the slope and intercept for graphing or you could use the equation and substitution to find another point on the line.

2a. The points have a strong negative correlation. This means that as x increases, y decreases.

2b. One example is the longer a candle burns, the shorter it gets. Another is the longer you run a car, the less gasoline is left in the tank.

2c. See students’ work.

3a.

50

55

60

65

70

75

80

'20'30'40'50'60'70'80 '90 '00Year of Birth

Life

Exp

ecta

ncy

(yea

rs)

3b. While students’ knowledge from other experiences may lead them to that conclusion, there may be other factors that contribute to increased longevity. The information on the graph only leads us to claim that life expectancy is increasing.

3c. A regression equation calculated by a graphing calculator would yield a prediction of 78.9 years. However, students may look at the era since 1980 and notice that each 5-year period is about 0.3 year less than the previous 5-year period increase. This pattern would yield a prediction of about 75.9 years.

In addition to the scoring rubric found on page A31, the following sample answers may be used as guidance in evaluating extended-response assessment items.

Chapter 4 Assessment Answer Key Page 67, Extended-Response Test

Sample Answers


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1. A B C D

2. F G H J

3. A B C D

4. F G H J

5. A B C D

6. F G H J

7. A B C D

8. F G H J

9. A B C D

10. F G H J

Chapter 4 Assessment Answer KeyStandardized Test PracticePage 68 Page 69

11. A B C D

12. F G H J

13. A B C D

14. F G H J

15. 16.

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

. . . . .

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

21 9

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

. . . . .

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

.8


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Chapter 4 Assessment Answer KeyStandardized Test PracticePage 70

17. 2r2t2

18. 0

19. -18

20. 21

21. 32

22. 16

23. -30 y

24. -2a + 3b

25. -8

26. 8 −

9

27. -7

28.

{-7.5, -6.5, -6,

-5, -3.5}

29.

Yes; exactly one member of the range is paired with each member of the

domain.

30. y =

3 −

2 x + 2

31. 5 −

7

32. y = -3x + 12

33. x = -6

34a. $2 per year

34b. $21.50


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