400Algebra 2H ASSIGNMENT SHEETrev14

CHAPTER 3: Linear Functions with Review of Chapter 1 and 2

(3-1 to 3-4 Highlights on reverse side)

Directions: 1. Review classwork and read each section in textbook before beginning written homework. Use

classwork problems and sample problems in text as a guide for homework problems.

Not all material on homework will be covered in class. As honor students, you need to learn to read

and understand the textbook as well as your class notes.

2. On top of each homework page please write the assignment number and page numbers.

3. Copy problem and show all work that leads to each answer.

4. Check your answers whenever possible with answers in back of textbook.

5. Note any topics and/or problems you would like to see reviewed the next day.

6. Bring math notebook, pencil, calculator and textbook to each class.

6. Remember: Upon arrival to class, open your notebook to assignment due that day and begin going over it

with your neighbor.

Sections to read Classwork / Homework:

and study:

#1 (Due day after Chapter 2 Test)

Complete Assignment #1 listed below on WK #1 in packet. Textbook required!!!

a) 3-1 to 3-4 Read p.73 – p.90 carefully. ALL of it should be review.

Use Chapter 3: 3-1 to 3-4 Highlights on reverse side as reference. Be sure to come for extra help if you need it. This is fast paced!!

b) 3-2 Refer to examples 1, 2, 3 pg.78-80: Do pg. 81 #1, 7, 9, 15, 17 (Remember: Complete on WK #1)

c) 3-3 Refer to example on pg.83: Do pg. 85 #1, 10, 11 (Complete on WK #1)

d) 3-4 Follow examples 1 and 2, pg.86-7.Use point-slope form first!: Do pg. 90 #5, 7 (Complete on WK #1)

#2 a) 3-4 Complete: 3-4 Equations of Linear Functions Class Lesson Wk #2

b) 3-4 Be sure to state each equation in point-slope, slope-intercept and standard form:

Do pg. 90 #1, 3, 9, 15-25odd Directions for Application Problems from 3-5:

Complete all parts of each problem AND be sure to include the following:

1) State equation in all 3 forms: point-slope, slope-intercept and standard form

2) State a reasonable range and domain in interval notation

3) Sketch graphs and label coordinates of at least 2 points (Graph paper not needed)

#3 a) 3-5 Complete: Using Linear Math Models to Predict Real World Information WK #3

b) 3-5 Be sure to follow directions above for Application Problems from 3-5: Do pg. 98 #5, 7, 15

c) Review Do pg. 46 #R3. a iii, iv / pg. 70 # R3.d / pg. 91 #13, 26 d) Bring TI Calculator to class tomorrow!!!!

#4a) Complete: Using TI Calculator: Linear Relationships Worksheet WK #5

Follow steps on Introduction to TI Calculator for Linear Functions WK #4 b) Review Do: Chapter 1, 2, 3 Review WK#6: #3-30, multiples of 3

#5a) Complete: Chapter 3: Class Lesson: Data Analysis – Estimating Line of Best Fit Wk#7 For TI-83 work, refer to Ch3: Directions for Data Analysis on TI-83- Line of Best Fit Wk#8

b) Complete: Ch. 3 Data Analysis on TI-83 – Line of Best Fit Assignment Wk#9

c) Review Do: Chapter 1, 2, 3 Review WK#6: # 33, 38, 39

Due day of Part 1 of Major Test: Data Analysis-Estimating Line of Best Fit (Calculator)

#6 Review Do: Chapter 1, 2, 3 Review WK#6: 2-38 evens

Due Day of Part 2 of Major Test on Chapters 1, 2, 3 (No calculator)

#7 Do: Chapter 1, 2, 3 Review WK#6: Complete all

Be sure to also review: Ch 1 Test, Ch 2 Test, and Ch 3 Highlights on reverse side

Alg2 Honors Chapter 3: 3-1 to 3-4 Highlights

Section 3-1: Linear Functions

A linear function is a function whose general equation is

y=mx+b

where m and b stand for constants, and m 0.

Section 3-2: Properties of Linear Function Graphs

The graphs of linear equations have the following properties:

1. The graphs are straight lines.

2. The value of m (the slope) determines how "tilted" the graph is:

a. If m is positive: Graph slopes up as x increases.

b. If m is negative: Graph slopes down as x increases.

3. If m is zero, the graph is horizontal, and therefore a constant function, not a linear function.

4. The value of b tells where the graph crosses the y-axis.

Intercepts:

1. The y-intercept of a function is the value of y when x = 0.

2. The x-intercept of a function is a value of x when y = 0.

m = Slope = rise = y2 – y1 = y Read: “delta y” over “delta x” OR

run x2 – x1 x “change in y” over “change in x”

Horizontal and Vertical Lines

1. If y = constant, then the graph is a horizontal straight line. The slope is 0.

2. If x = constant, then the graph is a vertical straight line. There is no number for the slope. The slope is

infinitely large (undefined).

Section 3-3: Other Forms of the Linear Function Equation

Forms of the Linear Function General Equation:

y = mx + b, slope-intercept form m = slope b = y intercept

y – y1 = m(x – x1) point-slope form (x1, y1) is a point on graph of line

Ax + By = C standard form A, B, C stand for relatively prime constants,

A ≥ 0

Section 3-4: Equations of Linear Functions from their Graphs

Parallel and Perpendicular Lines: If the equation of a line is y = mx + b, then:

A parallel line also has slope m

A perpendicular line has slope m

1

(p. 1 of 3) WK #1 Alg2H Chapter 3: Linear Functions: Assignment #1 TEXTBOOK REQUIRED!

a) 3-1 to 3-4 Read p.73 – p.90 carefully. ALL of it should be review. Use Chapter 3: 3-1 to 3-4 Highlights on reverse side of assignment sheet as reference.

b) 3-2 Be sure to refer to examples 1,2,3 p.78-80: p.81 1, 7, 9, 15, 17

p.81 #1 Write the equation: ___________________ #7 Write the equation: _____________

Plot the graph, using slope and y intercept Plot the graph, using slope and y intercept

#9 Write the equation: ________________

Plot the graph, using slope and y intercept

#15 Write the equation: ___________________ #17 Write the equation: __________

Plot the graph, Plot the graph,

WK#1 (p. 2 of 3)

c) 3-3 Be sure to refer to example on p.83: p.85 1, 10, 11

p.85 #1 Write the equation: ___________________

a) Plot graph, showing clearly the point and slope that appear in the equation.

b) Transform equation to slope-intercept form

c) Transform equation to Ax + By = C form, where A, B, and C are all integers

*and A is ____________________________

*and A, B, and C are _____________________

_____________________ (*to be filled in when in class)

p.85 #10 Write the equation: ___________________

a) Plot graph, showing clearly the point and slope that appear in the equation.

b) Transform equation to slope-intercept form

c) Transform equation to Ax + By = C form, where A, B, and C are all integers

(p. 3 of 3) WK#1

p.85 #11 Write the problem: _______________________________________________

Write an equation in point-slope form for the linear function described :

d) 3-4 Follow examples 1 and 2, p.86-7.Use point-slope form first!: p.90 5, 7

p.90 #5 Write the problem: _____________________________

a) Write the particular equation of the line described in point slope form: __________________

b) Transform the equation to slope-intercept form c) Transform the equation to Ax + By = C

form where A, B, C are integer constants

p.90 #7 Write the problem: _____________________________

a) Write the particular equation of the line described in point slope form: (Hint: Find slope first.)

b) Transform the equation to slope-intercept form c) Transform the equation to Ax + By = C

form where A, B, C are integer constants

ALG 2H 3-4 Equations of Linear Functions Class Lesson Worksheet WK #2 (p.1 of 2)

Parallel lines have ________________________________________ slope.

Perpendicular lines have ___________________________________ slopes.

1. a) Using slope and y-intercept, plot the graph of 2x + 5y = -5

b. Graph a line containing the point (-1, 2) and parallel to the graph of 2x + 5y = -5

c. Write the particular equation of the line described in (b) in point-slope form:

________________

d Transform to slope-intercept form: e. Transform to standard form (Ax + By = C where A, B, C are integer constants):

(A, B, C should be relatively prime to each other):

b. Graph a line containing the point (-1, 2) and perpendicular to the graph of 2x + 5y = -5

c. Write the particular equation of the line described in (b) in point-slope form:

________________

d Transform to slope-intercept form: e. Transform to standard form (Ax + By = C where A, B, C are integer constants):

(A, B, C should be relatively prime to each other):

WK #2 (p.2 of 2)

2. Graph and write the particular equation in as many forms as possible for each of the

following:

a. A linear function whose graph is a b. A linear function whose graph is a

vertical line and contains the point (2, -6) Horizontal line and contains the point (2, -6)

c. A linear function containing (-1, -5) and (3, -2)

d. A linear function with an x-intercept of -4 and perpendicular to the graph of 3x – 2y = 7

(p. 1 of 4) Wk #3 Alg2H Ch 3: Using Linear Mathematical Models to Predict Real World Information

1. Calvin Butterball drives from his home on the farm to nearby town of Scorpion Gulch. As he

drives, his distance from Scorpion Gulch depends on the number of minutes he has been driving.

When he has been driving 6 minutes, he is 17 km away; when he has been driving for 15

minutes, he is 11km away.

Use related, appropriate variables to represent each:

Independent variable: Let __ = ___________________________________________

Dependent variable: Let __ = ___________________________________________

a. Write the information about distances and times as two ordered pairs:

b. Label the horizontal and vertical axes with

names and units of measure of the

independent and dependent variables.

Plot the two ordered pairs

c. Assuming that the distance-time relation is

a linear function, determine related slope

(Ratio of the change in the dependent variable to

the change in the independent variable)

m =

e. Write the particular equation for this function:

(1) First use point-slope form. (Formula: ______________________________)

(2) Transform the equation to slope-intercept form. (Formula: ______________________)

e. Determine and label the distance-intercept and tell what it represents in the real world.

WK3 (p. 2 of 4) Re-write the equation:

f. Graph the linear function using the

slope-intercept form. (Does it go through the original 2 points?)

g. Use the equation to predict each:

(1) Calvin’s distance from Scorpion Gulch

when he has been driving for 24 minutes

(2) the time when Calvin arrives at Scorpion Gulch.

h. Write a reasonable domain and range in words using units of measure and in interval notation:

D:______________________________________________________ D: {__: }

R: ______________________________________________________ R: {__: }

i. Tell what the slope represents in the real world, and tell the significance of the fact that the

slope is negative.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Parallel and Perpendicular Lines

2. Suppose Phoebe Small drives from her home to nearby Scorpion Gulch. When she is 5 km

away from Scorpion Gulch, she notices that she has been traveling for 3 minutes. Assume that

this distance-time relation is a linear function and Phoebe discovers that its graph is parallel to

Calvin’s.

(1) What is the slope of the particular equation expressing her distance in terms of her time? ____

(Parallel lines have _______________ slope.)

(2) Determine that particular equation.

Summary of Problem: Given a point, determine an equation of a line parallel to the graph of a

given equation.

(p. 3 of 4)WK #3

Perpendicular Lines:

Here’s a challenging problem at the level you will find on the Chapter 1, 2, 3 test!!

3. Find the value of a such that the line x = 22w

will be perpendicular to the line that

has an x intercept of and goes through the point

(Over)

(p. 4 of 4)WK #3

4. A graph of a linear function has x-intercept of 5 and is perpendicular to the graph

of 4x + 3y = 15.

a. Write the particular equation of the line described in point-slope form:

b. Transform to slope-intercept form:

c. Transform to standard form:

5. Write the particular equation in as many forms as possible for each of the following:

a. A graph of a linear function is horizontal b. A graph of a linear function is vertical

and contains the point (-3, 11) and contains the point (-3,11)

WK #4 (p. 1 of 2)

Alg2H Introduction to Using the TI Calculator for Linear Functions

1) Enter the slope-intercept form of equation in the “y=” menu.

Only functions with = signs highlighted will be graphed.

2) Set WINDOW:

Xmin and Xmax corresponds to the domain. Ymin and Ymax corresponds to the range.

Xscl and Yscl can be set to appropriate scales for each axis.

Using the Zoom menu:

Scrolling down to 6:Zstandard or typing “6” sets the calculator standard window and automatically shows graph

of highlighted functions with that window.

If it is not appropriate, go to WINDOW and change it.

Make window larger to be able to see beyond the actual graph.

Use appropriate Xscl and Yscl to see graph.

If feasible, include negative values for Xmin and Ymin to see all quadrants on graph.

Experiment. Change the values of each of these and see how the graph is affected. Choose the most appropriate

setting for the particular problem.

3) Use GRAPH key to view highlighted functions in “y=” menu.

When copying a graph from the calculator to your paper, be sure to clearly label the axes, the scales and the

ordered pairs of appropriate points.

4) Use TRACE

When graph is on screen, press TRACE. Using the left and right arrows cursor can be moved along graph.

Coordinates of the points traced will show on bottom of screen. Try to find the points given or determined in the

problem to verify that they are on your graph.

If there are two or more functions graphed on the screen, the up and down arrows move the cursor from one graph to

another.

When you are not using TRACE, the cursor is a free to move anywhere on the screen using all the arrow keys.

Before using calculator:

Check MODE: All terms to left should be highlighted now. (If in Geometry, highlight Degrees)

Check FORMAT (2nd ZOOM): All terms on left should be highlighted now. (Games often shut off axes)

Check STAT PLOT (2nd “Y=”): All should be off.

WK #4 (p. 2 of 2)

5) Use the TABLE

a) TBLSET (2nd WINDOW) allows you to start a table with a chosen independent variable’s value (TblStart ) in

chosen increments (Tbl).

To see a full table, Independent and Dependent variables should be set with AUTO highlighted.

b) View the table by pressing TABLE (2nd Graph) . Use the up and down arrow keys to scroll up a column. Use the left

and right arrow keys to change columns. Verify that you can scroll to values before and after where the table was set.

Verify that all the ordered pairs of the problem can be found in your table. What might be wrong if an ordered pair of

the problem is not the same in the table? (Make any changes in your answers if necessary.)

c) To find the dependent value of a particular independent variable, go back to TBLSET and set Indpnt to Ask by

highlighting it and pressing enter. Leave the dependent variable with Auto highlighted.

Now when viewing the TABLE you can enter any values for the independent variable to find the corresponding

dependent values.

Spend some time exploring these features of the calculator and getting used to them. For each linear mathematical

model problem in section 3-5 use these features of the calculator appropriately to help you complete and

increase your understanding of the problem.

WK #5 (p. 1 of 2)

Alg2H Using the TI Calculator – Linear Relationships Preparation

Check the mode of your TI calculator. All terms to the left should be highlighted. (If you are taking

Geometry, highlight DEGREES.)

Purpose

To investigate a situation involving a linear relationship between two variables.

Background

Definition: Two changing quantities x and y are linearly related if y = ax + b where a and b are real

number constants.

Problem Situation: You know, from actual driving data, that your car gets 17 miles per gallon

when your average speed is 45 m.p.h., but only 14 m.p.g. when you average 60 m.p.h. A friend tells

you that mileage g is almost linearly related to average speed v when v is between 30 m.p.h. and 100

m.p.h. That is, for these speeds, g can be approximated as a linear function of v.

Identify: Independent variable:____ = _____________________________

Dependent variable: ____ = _____________________________

Investigations

1. Write the two ordered pairs defined by the given data. Use speed as input and gas mileage as

output.

2. Find the slope of the line defined by the linear relationship. Show your work.

3. Write the linear relationship described by the given data. Show your work.

point-slope form slope-intercept form Standard form

4. Enter your equation in the “y=” menu

Go to TBLSET (2nd-Window). Create a table that displays the gas mileage for each value of speed

from 50 m.p.h. to 80 m.p.h. in increments of 5 m.p.h. (ΔTbl = 5). (Both Independent and Dependent

variables should be set to Auto). To view the table go to TABLE (2nd-Graph)

average speed v

(m.p.h.)

gas mileage g

(m.p.g.)

WK #5 (p. 2 of 2)

5. In terms of gas mileage and speed, describe the meaning of the slope in this problem situation.

6. a. Write the domain of the problem situation. (Hint: See the description of the problem situation.)

b. Write the range of the problem situation. Give reasons for your answer.

7. Use your calculator to sketch the graph of the relationship over the domain of the problem situation.

Clearly label the axes, the scales, and each point from Table 1. (Follow the steps on the calculator

introduction sheet.)

8. What average speeds would give you gas mileage of at least 16 miles per gallon? Describe how

you found the answer.

9. Can the function created in investigation 3 be used to predict the gas mileage if the average speed is

25 m.p.h.? Why or why not? (Hint: What mileage does the function predict when the speed is zero?

Does this make sense?)

10. For each one m.p.h. increase in speed between 30 m.p.h. and 100 m.p.h., what happens to the gas

mileage? Give reasons for your answer.

Algebra 2 Honors Chapters 1, 2 and 3 Review WK#6 Date _____ WK6(p1of 8)

Complete all problems on a separate sheet of paper

Plot the graph of the given equation in the indicated domain. State the domain and range in interval

notation and determine if it is a function. (Graph without calculator first. Use calculator to check your

work, if possible.)

1. 2x –3y = -12; { -3 < x < 6 }

2. x2 + y = 3; {reals}

3. x + y2 = 3; {values of x for which there are real values of y}

x

y

x

y

x

y

4. y = |x| - 2 ; { -3 < x < 5} WK6(p.2 of 8)

5. |y| = 4 – 2x; {values of x for which there are real values of y}

6. 5x + 2y = 6 {whole numbers}

x

y

x

y

x

y

7. y = |x – 2 | {reals} WK6(p.3 of 8)

8. y = x

20; {values of x for which there are real values of y}

9. y =x

4 ; {negative numbers}

x

y

x

y

x

y

Tell whether or not the relation graphed is a function. WK6 (p.4 of 8)

10. 11.

12. 13.

Identify each polynomial by degree and term. If it is not a polynomial, explain why.

14. a. 3x2 – 4y 15. a. 4 - |3x|

b. x2y + 2xy – 3y2 b. 23abc

Tell the domain and range of the relation using inequality notation and interval notation:

16. 17.

Sketch a reasonable graph showing how the dependent variable is related to the independent variable.

Label horizontal and vertical axis in words and in appropriate units.

Write a few sentences defending your graph.

18. As you play with a yo-yo, the number of seconds that have passed and the yo-yo’s distance from

the floor are related.

19. You run the mile once each day. The number of times you have run it in practice and the length of

time it takes you to run are related.

10

-6

-8 -4

-3 -2 5

4

20. You take a roast beef from the refrigerator and put it into a hot oven. The temperature WK6(p.5 of 8)

of the beef and on how long it has been in the oven are related. (See example 2, p.60 for solution)

Give an example of each of the following:

21. a. an irrational number greater than one but less than two

b. a non-integer c. an imaginary number

22. a. a negative odd number b. a transcendental number

c. a digit that is not a counting number.

23. a. a natural number that is negative b. a rational number between 5/11 and 5/12

c. a real number that is also irrational

Solve, write the solution set and graph on the number line for each given domain:

24. 3 < 5 – 2x < 31 a) D: {whole numbers } b) D: {negative real numbers }

25. |x – 10| > -3 a) D: { integers } c) D: { non-negative reals}

26. 1 < | 2x + 8 | < 6 a) D: {real numbers} b) D : {negative integers}

27. 15 < | 15 – 5x | < 31 a) D: {real numbers } b) D: {natural numbers}

Find the equation of the described line in: WK6( p.6 of 8)

Point-slope form, Slope-intercept, Standard form (with integer coefficients)

28. Through (-6,3) and parallel to 3x – 9y = 14 (Graph the determined line and the given line on calculator.

Check if they look parallel.)

29. Through (-3,-8) and perpendicular to y = (-3/4) x + 5 (Graph the determined line and the given line on calculator.

Since axis on calculator are rectangular, go to ZOOM 6:Zsquare to make them square in order to check if

lines look perpendicular. )

30. Has an x-intercept of 3 and a y-intercept of –5

31. Vertical through (-2,3) 32. Horizontal through (-11,4)

Complete 33-36 on separate sheet of paper!!!!!!!!!!!!!!!!!!!!!! WK6(p.7 of 8)

Complete problems #33-#36 using the TI calculator. For each problem:

(1) Answer all questions asked.

(2) If not already asked in the problem, state a reasonable domain and range in interval notation.

(3) Graph the equation on your calculator.

(4) State the best values you used for your WINDOW settings in order to view the domain, range AND

all four quadrants.

(5) If not already asked in the problem, on your paper, sketch the graph in the appropriate domain and

range. Clearly label the axis, scales and coordinates of significant points.

33. p.98 #20 Direct Variation 34. p.98 #11

35. Elevator Problem: the number of feet of cable needed for an elevator depends on the number of

stories in the building it serves. Suppose that c= 20x + 35, where c is the number of feet of

elevator cable and s is the number of stories.

a. How do you know that c varies linearly with s?

b. How much cable is needed for a 29 story building?

c. How tall a building needs 375 feet of cable?

d. What does the slope represent in the real world?

e. What does the c-intercept equal? Why do you suppose that it is greater than zero?

f. Write a suitable domain and range for the linear function.

g. Plot the graph of this function, observing the domain you wrote in part f.

36. Ice Cube Problem: You run some water into a pitcher, then cool it down by adding ice cubes. You

find that putting in 5 cubes cools the water down to 66F. Putting in a total of 15 cubes cools down the

water to 48F. Assume that the temperature of the water varies linearly with the number of cubes you

put in.

a. Write the particular equation expressing temperature in terms of number of cubes.

b. Predict the temperature to which the water would cool if you had put in a total of:

(i) 7 cubes

(ii.) 10 cubes

(iii) 20 cubes

c. What total number of cubes would have to be put in to reduce the water temperature to freezing

(32F)?

d. What is the temperature-intercept? What does this number represent in the real world?

e. Water will not cool below freezing no matter how many cubes are put in. Plot the graph of this

linear function in a suitable domain.

f. Explain what the slope means in the real world.

g. State a reasonable domain and range in interval notation.

WITHOUTCALCULATOR: Simplify / Evaluate for A = -2, B = 5 , C = -3, D = ¼

37. 2 – 3(C + B) 38. (A – C)2 – 2(B – C2 + A)

5D

39. Bathtub Problem WK6(p.8 of 8)

You pull out the plug from your bathtub. After 40 seconds, there are 13 gallons of water left in the

tub. One minute after you pull the plug, there are 10 gallons left. Assume that the number of gallons

varies linearly with time since the plug was pulled.

1. Write the particular equation expressing number of gallons left in the tub in terms of number of

seconds since you pulled the plug. (State in all 3 forms.)

2. How many gallons would be left after

a. 20 seconds?

b. 50 seconds?

3. Find the gallons intercept. What does this number represent in the real world?

4. Find the time-intercept. What does this number represent in the real world?

5. Sketch the graph of this linear function. Use a suitable domain.

State the Domain and Range in interval notation.

6. What are the units of the slope? What does this number represent in the real world?

Alg2H Class Lesson: Data Analysis Date ______

Estimating Line of Best Fit Wk #7 (p. 1of 2)

Bean Stalk Problem: Jack plants a bean. Seven days

later it has sprouted and is 10 feet tall. On the 8th

through 15th days it heights are 17, 20, 25, 25, 32, 36, 38,

and 44 feet, respectively. Obviously, the number of

days since the bean was planted and the number of feet

tall are related.

a. Define

independent variable:

_______________________________________

dependent variable:

________________________________________

b. Complete the table of ordered pairs and plot the

associated points. Be sure to label each axis.

c. Using a straight edge, draw a straight line that seems

to “fit” the points the best. Extend it until it crosses

both the horizontal and vertical axes.

d. From the graph, estimate the slope and the y-

intercept. Use these to write an equation expressing

height in terms of time.

e. Using your equation, approximately when did the beanstalk first emerge from the ground?

f. Using your equation, approximately when will the bean stalk be 100 feet high?

Data Analysis using TI-83Plus WK#7 (p. 2 of 2)

g. Use the same set of data points listed in the table in part (b)

and follow the directions on the handout:

Ch. 3 Directions for Data Analysis on TI-Calculator – Line of Best Fit WK #8

to graph the data on the calculator and have the calculator find the line of best fit using linear

regression.

h. After you have the linear regression line in Y1 and have seen that line graphed through the data

points, compare it to your approximate equation in determined in part (d). Enter your approximate

equation in Y2 and graph that also.

i. When you have completed this classwork, start the homework worksheet:

Ch. 3 Data Analysis on TI-Calculator – Line of Best Fit Assignment Wk#9

This exercise uses actual data obtained from a National Vital Statistics Report on life

expectancy posted on the internet.

Continue to refer to the Directions for Data Analysis Wk #8 used above.

Alg2H Chapter 3: Directions for Data Analysis on TI-Calculator - Line of Best Fit WK#8

1. Press STAT. Under EDIT menu, choose 1:Edit... press ENTER

2. If you have data in any lists, highlight the list name (i.e. L1), press CLEAR and press ENTER to

clear the list.

3. Enter the data for the first variable in L1

Enter the data for the second variable in L2

4. Press STAT PLOT (2nd Y =) and Choose 1: and press ENTER

Highlight ON

Type: Choose 1st graph (scatter plot),

Xlist: L1 (2nd 1)

Ylist: L2 (2nd 2)

Mark: 3rd dot

5. Set Window to fit your data points or

press ZOOM and choose 9:ZoomStat to let the calculator do it.

6. Press GRAPH to see the scatter plot.

7. To determine the line of best fit, press STAT. Under CALC menu, choose

4:LinReg(ax + b) for data that looks linear.

(Realize that all data does not fit a linear model. Other regression equations can be used for data

that may be more quadratic, cubic, etc.)

8. When LinReg(ax+b) appears on the main screen, type L1, L2 right after it (look for the comma

button and use it!) and press ENTER. (These are the lists used in this example for the xlist and

ylist. If in a different example other lists are used, type the appropriate names.)

9. To graph this regression equation,

a) Press Y=

b) Clear Y1 and clear or de-highlight any other equations, if necessary.

c) Leave cursor after Y1=.

d) Press VARS. Under the VARS menu, chose 5:Statistics.....

e) Under EQ, choose 1:RegEq

f) The regression equation should now be copied into the Y1 equation.

10. Press GRAPH to see the graph of the regression equation (“line of best fit”) through the scatter

plot of the analyzed data.

Alg2H Ch. 3 Data Analysis on TI-83 – Line of Best Fit Assignment Wk#9

Name: ___________________________Date: _____________________

This assignment extends the TI Interactive! Data Analysis lesson. You will use your TI-83 calculator

to find the line of best fit using information from the National Vital Statistics Report on the next page.

A. Make a scatter plot comparing the year white females were born to their life expectancies.

1. Refer to the Directions for Data Analysis on the TI calculator WK#8 steps 1-3. In L1, begin with

40 (this corresponds to the year 1940) and enter the years in multiples of 5 (40, 45, 50…95).

2. In L2, enter the life expectancies for white females which correspond to the years in L1.

3. Continue with steps 4-10 on Directions for Data Analysis on the TI-83.

4. Write the equation you obtained:

5. Predict the life expectancy of a white female born the year 2000.

B. Make a scatter plot comparing the year black males were born to their life expectancies.

1. Refer to the Directions for Data Analysis on the TI-83 steps 1-3. In L1, begin with 40 (this

corresponds to the year 1940) and enter the years in multiples of 5 (40, 45, 50…95).

2. In L2, enter the life expectancies for black males which correspond to the years in L1.

3. Continue with steps 4-10 on Directions for Data Analysis on the TI-83.

4. Write the equation you obtained:

5. Predict the life expectancy of a black male born the year 2000.

C. Exploration questions.

1. What does the slope of each equation tell us about the data? What are the units of the slope?

2. Which population is improving their life expectancy faster? Justify your answer.

WK #10