chapter 4: linear functions and relations · obj: 4-1.1 write and graph linear equations in...

Chapter 4: Linear Functions and Relations

MULTIPLE CHOICE

Write an equation of the line with the given slope and y-intercept

1. slope: 2

7, y-intercept: –3

a. y = 2

7x – 3 c. y =

2

7x + 3

b. y = 7

2x – 3 d. y =

2

7x – 3

ANS: D

The linear equation y = mx + b is written in slope-intercept form, where m is the slope and b is the

y-intercept.

Feedback

A What is the slope of the line? B What is the slope? C What is the y-intercept? D Correct!

PTS: 1 DIF: Basic REF: Lesson 4-1

OBJ: 4-1.1 Write and graph linear equations in slope-intercept form.

NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4 STA: OK 2.3 | OK 2.5a | OK 2.5b

TOP: Write and graph linear equations in slope-intercept form

KEY: Slope-Intercept Form | Linear Equations | Graphs

2. slope: 0.8, y-intercept: 10

a. y = –0.8x + 10 c. y = 0.8x + 10

b. y = 0.8x – 10 d. y = 5

7x + 10

ANS: C


y-intercept.

Feedback

A What is the slope? B What is the y-intercept? C Correct! D What is the slope of the line?


OBJ: 4-1.1 Write and graph linear equations in slope-intercept form.

NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4 STA: OK 2.3 | OK 2.5a | OK 2.5b

TOP: Write and graph linear equations in slope-intercept form

KEY: Slope-Intercept Form | Linear Equations | Graphs

Beach Bike Rentals charges $5.00 plus $0.20 per mile to rent a bicycle.

3. Write an equation for the total cost C of renting a bicycle and riding for m miles.

a. c.

b. d.

ANS: A

If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The

y-intercept represents a starting point, and the slope represents the rate of change.

Feedback

A Correct! B Which number would be the y-intercept in the linear equation? C Which variable should be the independent variable? D What is the rate of change?


OBJ: 4-1.2 Model real-world data with an equation in slope-intercept form.

NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3

STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c

TOP: Model real-world data with an equation in slope-intercept form

KEY: Slope-Intercept Form | Equations | Real-World Problems

4. Graph the equation needed to represent the cost at Beach Bike Rentals.

a.

1 2 3 4 5 6 7 8 9 10 m

1

2

3

4

5

6

7

8

9

10C

b.

1 2 3 4 5 6 7 8 9 10 m

1

2

3

4

5

6

7

8

9

10C

c.

1 2 3 4 5 6 7 8 9 10 m

1

2

3

4

5

6

7

8

9

10C

d.

1 2 3 4 5 6 7 8 9 10 m

1

2

3

4

5

6

7

8

9

10C

ANS: B



Feedback

A Is the rate of change positive or negative? B Correct! C What is the y-intercept? D What is the base rental cost?

PTS: 1 DIF: Average REF: Lesson 4-1


NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3




5. What is the cost of renting a bike and riding 18 miles?

a. $3.60 c. $8.60

b. $41.00 d. $11.60

ANS: C



Feedback

A Did you forget the base rate for bike rental? B What is the rate per mile? C Correct! D What was the base rate for bike rental?



NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3




Write a linear equation in slope-intercept form to model the situation.

6. A television repair shop charges $35 plus $20 per hour.

a. c. b. d.

ANS: D



Feedback

A Which number represents the intercept? B Which variable is the independent variable? C What is the slope? D Correct!



NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3




7. An icicle is 12 inches long and melts at a rate of inch per hour.

a. c.

b. d.

ANS: A



Feedback

A Correct! B What was the original length of the icicle? C What is the rate of change? D Which variable is the independent variable?



NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3




8. The temperature is 38 and is expected to rise at a rate of 3 per hour.

a. c. b. d.

ANS: B



Feedback

A What is the starting temperature? B Correct! C Is the temperature decreasing? D Which variable is the independent variable?



NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3




9. A taxi driver charges $5 plus $0.30 per mile.

a. c. b. d.

ANS: C



Feedback

A What is the base price? B Does the cost go down with additional miles? C Correct! D Which variable is the independent variable?



NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3




Mr. Collins is constructing a fence around his property. He already has 25 sections up and plans to

add 8 sections each Saturday until he is finished.

10. Write an equation to find the total number of fence sections F standing after any number of

Saturdays s.

a. c. b. d.

ANS: A



Feedback

A Correct! B How many sections are already up? C Does the number of sections standing decrease each Saturday? D Which variable is the independent variable?



NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3




11. Graph the equation for the number of fence sections F standing after any number of Saturdays s.

a.

Saturdays

Fen

ce S

ections

1 2 3 4 5 6 7 8 9 10 s

10

20

30

40

50

60

70

80

90

100

110

F

b.

Saturdays

Fen

ce S

ections

1 2 3 4 5 6 7 8 9 10 s

10

20

30

40

50

60

70

80

90

100

110

F

c.

Saturdays

Fen

ce S

ections

1 2 3 4 5 6 7 8 9 10 s

10

20

30

40

50

60

70

80

90

100

110

F

d.

Saturdays

Fen

ce S

ections

1 2 3 4 5 6 7 8 9 10 s

10

20

30

40

50

60

70

80

90

100

110

F

ANS: A



Feedback

A Correct! B What is the y-intercept? C Does the number of sections standing decrease each Saturday? D What is the slope of the line?



NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3




12. Find the total number of fence sections standing after 15 Saturdays.

a. 383 sections c. 145 sections

b. 125 sections d. 105 sections

ANS: C



Feedback

A How many sections did he install each Saturday? B How many sections were standing at the beginning? C Correct! D How many Saturdays did you use?



NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3




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

13.

a. c.

b. d.

ANS: D

Find the y-intercept by replacing x and y with the given point and m with the given slope in the

slope-intercept form. Solve for b. Write the equation in slope-intercept form using the given m and the

calculated b.

Feedback

A What is the y-intercept? B What is the y-intercept? C What is the slope of the line? D Correct!


OBJ: 4-2.1 Write an equation of a line given the slope and one point on the line.

NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3


TOP: Write an equation of a line given the slope and one point on a line

KEY: Slope | Equations | Lines

14.

a. c.

b. d.

ANS: B

Find the y-intercept by replacing x and y with the given point and m with the given slope in the

slope-intercept form. Solve for b. Write the equation in slope-intercept form using the given m and the

calculated b.

Feedback

A What is the slope of the line? B Correct!

C What is the y-intercept? D What is the y-intercept?


OBJ: 4-2.1 Write an equation of a line given the slope and one point on the line.

NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3


TOP: Write an equation of a line given the slope and one point on a line

KEY: Slope | Equations | Lines

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

15.

a. y = 1

8x +

11

8 c. y =

1

8x –

11

8

b. y = 1

8x –

11

8 d. y =

1

8x +

8

11

ANS: B

Find the slope of the line with the slope formula. Find the y-intercept by replacing x and y with the

given point and m with the slope in the slope-intercept form. Solve for b. Write the equation in

slope-intercept form using the given m and the calculated b.

Feedback

A What is the y-intercept? B Correct! C Is the slope positive or negative? D How did you find the y-intercept?


OBJ: 4-2.2 Write an equation of a line given two points on the line.

NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6

STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b

TOP: Write an equation of a line given two points on the line KEY: Slope | Lines | Equations

16.

a. y = –8x + 22 c. y = 8x – 32

b. y = –8x + 32 d. y = –8x – 32

ANS: D




Feedback

A How did you find the y-intercept? B What is the y-intercept? C Is the slope positive or negative? D Correct!


OBJ: 4-2.2 Write an equation of a line given two points on the line.

NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6

STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b

TOP: Write an equation of a line given two points on the line KEY: Slope | Lines | Equations

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

17. (–4, 3), m = 1

a. y – 3 = 1(x + 4) c. y – 3 = 1(x – 4)

b. y + 3 = 1(x + 4) d. y – 3 = –(x + 4)

ANS: A

The linear equation is written in point-slope form, where is a given point

on a nonvertical line and m is the slope of the line.

Feedback

A Correct! B What is the y-coordinate of the given point? C Did you subtract the x-coordinate from x? D What is the slope of the line?


OBJ: 4-3.1 Write the equation of a line in point-slope form.

NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6

STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4c

TOP: Write the equation of a line in point-slope form

KEY: Point-Slope Form | Equations | Lines

18. (–6, –6), m = 4

7

a. y – 6 = 4

7(x + 6) c. y + 6 =

4

7(x + 6)

b. y + 6 = 4

7(x – 6) d. y + 6 =

4

7(x + 6)

ANS: D



Feedback

A What is the y-coordinate of the given point? B Did you subtract the x-coordinate from x? C What is the slope of the line? D Correct!


OBJ: 4-3.1 Write the equation of a line in point-slope form.

NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6

STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4c

TOP: Write the equation of a line in point-slope form

KEY: Point-Slope Form | Equations | Lines

Write each equation in standard form.

19. y + 6 = (x + 4)

a. x + y = –2 c. x – y = 2

b. y = x – 2 d. x – y = 10

ANS: C

Solve the equation for y. Use Addition and Subtraction Properties of Equality to rewrite the equation in

standard form.

Feedback

A How did you determine the sign of the y-term? B Is that standard form? C Correct! D Did you use the correct property of equality?


OBJ: 4-3.2 Write linear equations in standard form.

NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6

STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c

TOP: Write linear equations in standard form

KEY: Standard Form | Linear Equations

20. y + 3 = 2

5(x + 9)

a. 2x – 5y = 33 c. y = 2

5x +

3

5

b. 2x – 5y = –3 d. 2x + 5y = 3

ANS: B

Solve the equation for y. Use Addition and Subtraction Properties of Equality to rewrite the equation in

standard form.

Feedback

A Did you use the correct property of equality? B Correct! C Is that standard form? D How did you determine the sign of the y-term?


OBJ: 4-3.2 Write linear equations in standard form.

NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6


TOP: Write linear equations in standard form

KEY: Standard Form | Linear Equations

Write the equation in slope-intercept form.

21.

a. c.

b. d.

ANS: B

Given an equation in point-slope form, solve the equation for y to find the equation in slope-intercept

form.

Feedback

A What is the slope of the line? B Correct!

C How did you find the y-intercept? D What is the y-intercept of the equation?


OBJ: 4-3.3 Write linear equations in slope-intercept form.

NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6


TOP: Write linear equations in slope-intercept form

KEY: Slope-Intercept Form | Linear Equations

22. y – 5 = 3

4(x – 5)

a. y = 3

4x –

5

4 c. y =

3

4x +

5

4

b. y = 3

4x +

5

4 d. y =

3

4x –

3

5

ANS: B


form.

Feedback

A What is the y-intercept of the equation? B Correct! C What is the slope of the line? D How did you find the y-intercept?


OBJ: 4-3.3 Write linear equations in slope-intercept form.

NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6


TOP: Write linear equations in slope-intercept form

KEY: Slope-Intercept Form | Linear Equations

Write the slope-intercept form of an equation of the line that passes through the given point and is

parallel to the graph of the equation.

23. (5, –1), y = 3

4x + 1

a. y = 11

4x +

3

4

b. y = 4

3x +

11

5

c. y = 3

4x +

11

4

d. y = 3

4x –

11

4

ANS: C

Two nonvertical lines are parallel if they have the same slope. Use the given point with the slope of the

parallel line in the point-slope form. Then change to the slope-intercept form.

Feedback

A What is the slope of the parallel line? B Did you add or subtract carefully? Should the slope be the same as the slope of the

parallel line? C Correct!

D Be careful with signs when adding to or subtracting from both sides of the equation.


OBJ: 4-4.1 Write an equation of the line that passes through a given point, parallel to a given line.

NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6


TOP: Write an equation of the line that passes through a given point, parallel to a given line

KEY: Lines | Equations | Parallel

24. (–5, –3), 5x – 4y = 8

a. y = 5

4x +

13

4

b. y = 5

4x –

13

4

c. y = 4

5x +

13

5

d. y = 13

4x +

5

4

ANS: A



Feedback

A Correct! B Be careful with signs when adding to or subtracting from both sides of the equation. C Did you add or subtract carefully? Should the slope be the same as the slope of the

parallel line? D What is the slope of the parallel line?


OBJ: 4-4.1 Write an equation of the line that passes through a given point, parallel to a given line.

NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6


TOP: Write an equation of the line that passes through a given point, parallel to a given line

KEY: Lines | Equations | Parallel

Write the slope-intercept form of an equation that passes through the given point and is perpendicular

to the graph of the equation.

25. (4, 4), 2x – y = 4

a. y = 2x + 2

b. y = 1

2x + 6

c. y = 1

2x + 6

d. y = 4x + 2

ANS: B

Two nonvertical lines are perpendicular if the slopes are opposite reciprocals of each other. Use the

given point with the slope of the perpendicular line in point-slope form. Then change to slope-intercept

form.

Feedback

A Did you add or subtract carefully? Should the slope be the same as the slope of the

perpendicular line?

B Correct! C How are the slopes of perpendicular lines related? D What is the slope of the perpendicular line?


OBJ: 4-4.2 Write an equation of the line that passes through a given point, perpendicular to a given

line. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3

STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a

TOP: Write an equation of the line that passes through a given point, perpendicular to a given line

KEY: Lines | Equations | Perpendicular

26. (2, 2), y = 1

5x + 5

a. y = 1

5x – 2

b. y = 5x – 8

c. y = 5x – 8

d. y = 12

5x –

1

5

ANS: B



form.

Feedback

A Did you add or subtract carefully? Should the slope be the same as the slope of the

perpendicular line? B Correct! C How are the slopes of perpendicular lines related? D What is the slope of the perpendicular line?


OBJ: 4-4.2 Write an equation of the line that passes through a given point, perpendicular to a given

line. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3

STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a

TOP: Write an equation of the line that passes through a given point, perpendicular to a given line

KEY: Lines | Equations | Perpendicular

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.

27.

Women in the Army

Per

cent

1981 1991 2001

2

4

6

8

10

12

14

16

Year

Source: Time Magazine, March 24, 2003

a. positive; as time goes on, more women are in the army.

b. no correlation

c. negative; as time goes on, fewer women are in the army.

d. negative; as time goes on, more women are in the army.

ANS: A

A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane.

There is a positive correlation when as x increases, y increases. There is a negative correlation when as

x increases, y decreases. There is no correlation when x and y are not related.

Feedback

A Correct! B Are the variables related? C Is the number of women in the army decreasing? D What is meant by negative correlation?


OBJ: 4-5.1 Interpret points on a scatter plot.

NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3 STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a

TOP: Interpret points on a scatter plot KEY: Scatter Plot | Interpret Data

28.

Average Cycling Speed

Mil

es P

er H

our

M inutes5 10 15 20 25 30 35

2

4

6

8

10

12

14

16

18

a. no correlation

b. negative; as time passes, speed decreases

c. positive; as time passes, speed increases

d. positive; as time passes, speed decreases

ANS: B




Feedback

A Are the variables related? B Correct! C Is the speed increasing? D What is meant by positive correlation?





29.

Video Rental Fines

Fin

es (

do

llar

s)

Videos Rented1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

a. negative; as the number of videos rented increases, the amount of fine increases.

b. negative; as the number of videos rented increases, the amount of fine decreases.

c. no correlation

d. positive; as the number of videos rented increases, the amount of fine decreases.

ANS: C




Feedback

A What is meant by negative correlation? B Does the amount of fine decrease with the number of videos rented? C Correct! D What is meant by positive correlation?





30.

People Entering Amusement Park

Num

ber

of

Peo

ple

10 20 30 40 50 60 70 80 90 100

100

200

300

400

500

600

700

800

900

1000

Time (minutes)

a. positive; as time passes, the number of people entering decreases.

b. negative; as time passes, the number of people entering decreases.

c. no correlation

d. positive; as time passes, the number of people entering increases.

ANS: D




Feedback

A What is meant by positive correlation? B Does the number of people decrease as time passes? C Are the variables related? D Correct!





31.

Strawberries Picked

Quar

ts P

icked

1 2 3 4 5 6 7 8 9 10

10

20

30

40

50

60

70

80

90

100

Time (hours)

a. positive; as time passes, the number of quarts picked decreases.

b. negative; as time passes, the number of quarts picked decreases.

c. no correlation

d. positive; as time passes, the number of quarts picked increases.

ANS: B




Feedback

A What is meant by positive correlation? B Correct! C Are the variables related? D Does the number of quarts picked increase over time?





32.

United States Birth Rate (per 1000)

1990 1992 1994 1996 1998 2000

12

14

16

18

20

22

24

Year

Source: National Center for Health Statistics, U.S.

Dept. of Health and Human Services

a. no correlation

b. positive correlation; as time passes, the birth rate increases.

c. positive correlation; as time passes, the birth rate decreases.

d. negative correlation; as time passes, the birth rate decreases.

ANS: D




Feedback

A Are the variables not related? B Is the birth rate increasing with the passage of time? C What is mean by a positive correlation? D Correct!





33.

Consumer Price Index, 1950-2002

1950 1960 1970 1980 1990 2000

100

200

300

400

500

600

700

Year Source: Bureau of Labor Statistics, U.S. Dept. of Labor

a. no correlation

b. positive correlation; as time passes, the CPI increases.

c. positive correlation; as time passes, the CPI decreases.

d. negative correlation; as time passes, the CPI decreases.

ANS: B




Feedback

A Are the variables not related? B Correct! C What is meant by positive correlation? D Is the CPI decreasing?





34.

Sport Utility Vehicle Sales in the U.S.,

1991-2001

1990 1992 1994 1996 1998 2000 2002

1

2

3

4

5

6

7

Year Source: The World Almanac, 2003

a. negative correlation; as time passes, SUV sales decrease.

b. no correlation

c. positive correlation; as time passes, the SUV sales decrease.

d. positive correlation; as time passes, the SUV sales increase.

ANS: D




Feedback

A Are sales decreasing? B Are the variables not related? C What is meant by positive correlation? D Correct!





35.

Domestic Traveler Spending in the U.S., 1987-1999

1986 1988 1990 1992 1994 1996 1998

225

250

275

300

325

350

375

400

425

450


a. positive correlation; as time passes, spending increases.

b. no correlation

c. positive correlation; as time passes, spending decreases.

d. negative correlation; as time passes, spending decreases.

ANS: A




Feedback

A Correct! B Are the variables not related? C What is meant by positive correlation? D Is spending decreasing with time?





36.

Cars Passing School

Num

ber

of

Car

s

Hours1 2 3 4 5 6 7 8 9 10

10

20

30

40

50

60

70

80

90

100

a. negative; as time passes, the number of cars increases.

b. negative; as time passes, the number of cars decreases.

c. no correlation

d. positive; as time passes, the number of cars decreases.

ANS: C




Feedback

A What is meant by negative correlation? B Is the number of cars decreasing with the passage of time? C Correct! D What is meant by positive correlation?





United States Birth Rate

Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Birth Rate

(per 1000)

16.7

16.3

15.9

15.5

15.2

14.8

14.7

14.5

14.6

14.5

14.7

14.5 Source: National Center for Health Statistics, U.S. Dept. of Health and Human Services

37. Let x represent the number of years since 1990 with x = 0 representing 1990. Let y represent the birth

rate per 1000 population. Write the slope-intercept form of the equation for the line of fit using the

points representing 1992 and 2000.

a. c.

b. d.

ANS: A

If the data points do not all lie on a line, but are close to a line, you can draw a line of fit. This line

describes the trend of the data. Once you have a line of fit, you can find an equation of the line using 2

points to find the slope and y-intercept.

Feedback

A Correct! B Is there a positive correlation? C Did you subtract when you should have added? D Which variable is the independent variable?


OBJ: 4-5.2 Use lines of fit to make and evaluate predictions.

NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 STA: OK 2.1a | OK 2.2 | OK 2.3 | OK 2.4e | OK 3.1a

TOP: Write equations for lines of fit KEY: Best Fit Line | Equations

38. Predict the birthrate in 2005. Round your answer to the nearest tenth, if necessary.

a. 14.5 c. 15.1

b. 13.1 d. 14.0

ANS: D

Write an equation for the line of fit. Substitute to find a prediction for 2005.

Feedback

A Do you predict that the rate will remain unchanged from 2001? B Did you write an equation for the line of fit? C Do you predict the rate will increase from 2001? D Correct!





Domestic Traveler Spending in the U.S., 1987-1999

1986 1988 1990 1992 1994 1996 1998 2000

225

250

275

300

325

350

375

400

425

450


39. Use the scatter plot that shows the domestic traveler spending. Use the points (1987, 235) and

(1999, 446) to write the slope-intercept form of an equation for the line of fit shown in the scatter plot.

a. c.

b. d.

ANS: C

Use the two points to calculate the slope of the line. Then find the slope intercept form of the equation

of the line using the slope and one of the points.

Feedback

A Is the slope of the line of fit negative? B Which variable is the independent variable? C Correct! D How did you determine the slope of the line?





40. Use the scatter plot that shows the domestic traveler spending. Predict the amount of spending for

domestic travelers in 2010.

a. about $640,000,000 c. about $640

b. about $460,000,000,000 d. about $640,000,000,000

ANS: D



Feedback

A How do you read that amount? B Do you expect the amount of spending to decrease? C Did you read the graph carefully? D Correct!





Strawberries Picked

Quar

ts P

icked

Time (hours)1 2 3 4 5 6 7 8 9 10

10

20

30

40

50

60

70

80

90

100

41. Use the scatter plot that shows the number of quarts of strawberries picked each hour. Use the points

(1, 73) and (8, 41) to write the slope-intercept form of an equation for the line of fit shown in the

scatter plot.

a. c.

b. d.

ANS: D



Feedback

A Is the slope of the line of fit positive? B Which variable is the independent variable? C How did you determine the slope of the line? D Correct!





42. Use the scatter plot that shows the number of quarts of strawberries picked each hour. Predict the

number of quarts that will be picked in the tenth hour.

a. about 123 quarts c. about 32 quarts

b. about 45 quarts d. about 34 quarts

ANS: C


of the line using the slope and one of the points. Use the equation to make the prediction.

Feedback

A What is the slope in your equation? B Do you expect the number quarts to increase? C Correct! D Did you evaluate the equation carefully?





Average Cycling Speed

Mil

es P

er H

our

M inutes5 10 15 20 25 30 35

2

4

6

8

10

12

14

16

18

43. Use the scatter plot that shows the average cycling speed as time passes. Use the points (5, 15) and

(25, 10) to write the slope-intercept form of an equation for the line of fit shown in the scatter plot.

a. c.

b. d.

ANS: A



Feedback

A Correct! B Which variable is the independent variable? C Is the slope of the line of fit positive? D How did you determine the slope of the line?





44. Use the scatter plot that shows the average cycling speed as time passes. Predict the speed of the

cyclist after 30 minutes.

a. about 6.2 miles per hour c. about 12.3 miles per hour

b. about 8.8 miles per hour d. about 10.5 miles per hour

ANS: B



Feedback

A What is the slope in your equation? B Correct! C Do you expect the number quarts to increase? D Did you evaluate the equation carefully?





Sport Utility Vehicle Sales in the U.S., 1991-2001

Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Sales

(millions)

0.9

1.2

1.4

1.6

1.8

2.2

2.5

2.8

3.0

3.4

3.8 Source: The World Almanac, 2003

45. Let x represent the number of years since 1990. Let y represent the sport utility vehicle sales in

millions. Write the slope-intercept form of the equation for the line of fit using the points representing

1992 and 2000.

a. c.

b. d.

ANS: A


describes the trend of the data. Once you have a line of fit, you can find an equation of the line using 2

points to find the slope and y-intercept.

Feedback

A Correct! B Is there a negative correlation? C Did you add when you should have subtracted? D Which variable is the independent variable?





46. Predict the number of sport utility vehicle sales in 2005.

a. about 3.5 million c. about 2.4 million

b. about 4.8 million d. about 5.9 million

ANS: B



Feedback

A Do you expect sales to decline? B Correct! C What is the y-intercept? D What did you find to be the y-intercept?





Find the equation of the regression line.

47.

a. c.

b. d.

ANS: B PTS: 1 DIF: Basic REF: Lesson 4-6

OBJ: 4-6.1 Write equations of best-fit lines using linear regression.

STA: OK 3.1c TOP: Regression and median fit lines.

KEY: linear regression | best-fit line

Find y for the given value of x.

48. The best-fit line is . .

a. 8.55 c. 1.2

b. 8.05 d. 7.23

ANS: A PTS: 1 DIF: Basic REF: Lesson 4-6

OBJ: 4-6.1 Write equations of best-fit lines using linear regression.

STA: OK 3.1c TOP: Regression and median fit lines.

KEY: linear regression | best-fit line

Find the graph of the function.

49.

a.

2 4 6 8 10–2–4–6–8–10 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

c.

2 4 6 8 10–2–4–6–8–10 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

b.

2 4 6 8 10–2–4–6–8–10 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

d.

2 4 6 8 10–2–4–6–8–10 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

ANS: A PTS: 1 DIF: Basic REF: Lesson 4-7

OBJ: 4-7.1 Identify and graph absolute value functions. TOP: Special functions.

KEY: absolute value function

50.

a.

2 4 6 8 10–2–4–6–8–10 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

c.

2 4 6 8 10–2–4–6–8–10 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

b.

2 4 6 8 10–2–4–6–8–10 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

d.

2 4 6 8 10–2–4–6–8–10 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

ANS: C PTS: 1 DIF: Basic REF: Lesson 4-7

OBJ: 4-7.1 Identify and graph absolute value functions. TOP: Special functions.


SHORT ANSWER

1. Cindy started her bank account with $400, and she deposited $50 per week. Write a linear equation in

slope-intercept form to find the total amount in her account after w weeks. Then graph the equation.

ANS:

;

Am

ou

nt

($)

1 2 3 4 5 6 7 8 9 10 x

350

400

450

500

550

600

650

700

750

800

y

Week




OBJ: 4-1.3 Solve multi-step problems. NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3 | NA 8

STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c | OK 2.5a | OK 2.5b

TOP: Solve multi-step problems. KEY: Multi-step | Problem Solving

2. The cost of admission to an amusement park is $9.50 plus $1.50 per ride. Write a linear equation in

slope-intercept form for the amount spent if r rides are taken.

ANS:







3. Anthony is reading a book with 256 pages. He reads 14 pages every day. Write a linear equation in

slope-intercept form to find the number of pages left after d days.

ANS:







4. The monthly telephone bill consists of $24 service charge plus $1.20 per call. Write an equation in

slope-intercept form for the total monthly bill if x represents the number of calls made in a month.

Then graph the equation.

ANS:

;

Number of Calls

Month

ly B

ill ($

)

20 40 60 80 100 120 140 160 180 x

40

80

120

160

200

240

280

320

360

400y



PTS: 1 DIF: Advanced REF: Lesson 4-1




5. The cost, C, of joining the sports center gym includes an initial membership fee of $139 plus a $29

monthly fee. Write an equation in slope-intercept form to find the total cost for m months. Then graph

the equation.

ANS:

;

Co

st (

$)

1 2 3 4 5 6 7 8 9 10 x

100

150

200

250

300

350

400

450

500

550

y

Month







6. The table of ordered pairs shows the coordinates of the two points on the graph of a line.

x y

0 6

4 10

Write an equation that describes the line.

ANS:





OBJ: 4-2.3 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 3 | NA 4

STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c TOP: Solve multi-step problems.

KEY: Multi-step | Problem Solving

7. Write an equation and describe the slope for the line that passes through and .

ANS:

;








8. In 1992, about 12.5 million people were using broadband internet services. In 1999, the number was

17.4 million. Write a linear equation to predict the number of people, P, who will be using broadband

internet services in year t.

ANS:








9. Write an equation for the line that passes through and . What is the slope?

ANS:

; 2








10. A company manufactured 324,000 computers in 2002. The company’s output grows by 5,000 units per

year.

Year Production (thousands)

2002 324

2003 329

2004 334

Write a linear equation to find the company’s production, P, in year, t.

ANS:








11. Write the point-slope form, slope-intercept form, and standard form of an equation for a line that

passes through with slope 4.

ANS:

; ;




form.

The linear equation in standard form is given as , where A, B, and C are constants. Use

Addition and Subtraction Properties of Equality to rewrite the equation in standard form.


OBJ: 4-3.4 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6

STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c TOP: Solve multi-step problems.



passes through with slope –9.

ANS:

; ;




form.


Addition and Subtraction Properties of Equality to rewrite the equation in standard form.






passes through with slope .

ANS:

; ;




form.


Addition and Subtraction Properties of Equality to rewrite the equation in standard form. Remember

that A, B, and C must be integers with a GCF of 1.





14. Line l passes through with slope . Write the point-slope form, slope-intercept form, and

standard form of an equation for line l.

ANS:

; ;




form.








15. A line passes through with slope . Write the point-slope form, slope-intercept form, and

standard form of an equation for line l.

ANS:

; ;




form.








16. Determine whether and are perpendicular. Explain.

ANS:

No; the slopes are 4 and .

Two nonvertical lines are perpendicular if the slopes are opposite reciprocals of each other.



STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c | OK 2.4a | OK 2.5a


17. Write an equation of the line that is parallel to the graph of and passes through .

ANS:







18. Find an equation for the line that has an x-intercept of 3 and is perpendicular to the graph of

.

ANS:

or



form.





19. Determine the relationship between the diagonals and of rhombus PQRS with ,

, , and .

ANS:

They are perpendicular because the slopes are and .

Two nonvertical lines are parallel if they have the same slope.






20. Write the slope-intercept form of an equation for the line that passes through and is

perpendicular to the graph of the equation .

ANS:



form.





The table shows the age of infants, t (in weeks), and the number of hours, h, they slept in a day.

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

ANS:

Sle

ep (

ho

urs

per

day

)

3 6 9 12 15 18 21 24 t

13

13.5

14

14.5

15

15.5

16

16.5

h

Age (in weeks)

Negative correlation.


There is a positive correlation when y increases as x increases. There is a negative correlation when y

decreases as x increases. There is no correlation when x and y are not related.



STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a | OK 2.1a | OK 2.4e | OK 3.1a


22. Suppose a child is 2 years old. Would the equation for the line of fit give a reasonable estimate of the

number of hours slept in a day by a child of that age? Explain.

ANS:

No; using the equation would give 2.82 hrs of sleep in a day, which is not a reasonable estimate for a

2-year-old.

Write an equation for the line of fit. Use the equation to make the prediction.





23. The table below shows Alex’s best time for the 200-m sprint each year.

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

ANS:

Tim

e (s

)

1989 1990 1991 1992 1993 1994 1995 1996 x

28

29

30

31

32

33

34

35

36

37

y

Year

Positive correlation








24. The graph below shows the relationship between a long-distance truck driver’s driving times and the

number of miles traveled.

Dis

tan

ce t

rav

eled

(m

i)

60 75 90 105 120 135 150 165 180 x

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

y

Driving time (h)

Is it reasonable to use the equation for line of fit to estimate the distance traveled for a driving time of

10 hours? Explain.

ANS:

No; using the equation would give –333.3 miles, which is not a reasonable estimate.

Write an equation for the line of fit. Use the equation to make the prediction.





25. The table below shows the time in hours an investor spent researching the stock market each week and

the percent gain on investments.

Make a scatter plot and draw a line of fit for the data.

ANS:

Gai

n (

%)

2 4 6 8 10 12 14 16 18 20 x

20

24

28

32

36

40

44

48

52

56

y

Time (h)





describes the trend of the data.





26.

Year 2001 2002 2003 2004 2005 2006

Sales ($1,000) 253 242 265 270 269 275

Write an equation of the regression line in the form of . Estimate the sales for 2010.

ANS:

; $298,730


OBJ: 4-6.2 Solve multi-step problems. STA: OK 3.1c

TOP: Regression and median fit lines. KEY: linear regression | best-fit line

27.

Game 1 2 3 4 5 6

Score 85 82 83 80 78 75

Write an equation of the best-fit line in the form of . Estimate the score for the 15th game.

ANS:

; 59.1




28.

Year 1 2 3 4 5 6

Height (ft) 4 10 15 27 51 60

Write an equation of the regression line in the form of . Estimate the height when the tree is

8 years old.

ANS:

; 81.21 feet




29.

Month 1 2 3 4 5 6

Units Produced 275 400 612 867 1,020 1,465

Write an equation of the best-fit line in the form of . Name the correlation coefficient.

Round to the nearest ten-thousandth.

ANS:

; 0.983



TOP: Regression and median fit lines.

KEY: linear regression | best-fit line | correlation coefficient

30.

Place 1 2 3 4 5 6

Score 9.89 9.75 9.72 9.61 9.55 9.42

Write the equation of a median-fit line in the form of . Predict the score of 10th place.

ANS:

; 9.15



TOP: Regression and median fit lines. KEY: linear regression | median-fit line

Write the function and state the domain and range.

31.

ANS:

domain is all real numbers

range is


OBJ: 4-7.2 Solve multi-step problems. TOP: Special functions.

KEY: piecewise-defined function

32.

ANS:


range is all integers



KEY: greatest integer function

33.

ANS:


range is




34.

ANS:


range is all integers



KEY: greatest integer function

35.

ANS:


range is




ESSAY

1. Mary charges a flat fee of $5 plus $2 per hour for baby-sitting.

a. Explain how y-intercepts can be used to describe real-world costs.

b. Write a description of a situation in which the y-intercept of its graph is $7.50.

ANS:

Sample answer:

a. The y-intercept is the flat fee in an equation that represents a price.

b. If Mary charges $7.50 as the flat fee plus $2 per hour for babysitting, the graph representing this

situation would have a y-intercept of $7.50.


y-intercept. If a quantity changes at a constant rate over time, it can be modeled by a linear function.

The y-intercept represents a starting point, and the slope represents the rate of change.

Assessment Rubric

Level 3 Superior *Shows thorough understanding of concepts.

*Uses appropriate strategies.

*Computation is correct.

*Written explanation is exemplary.

*Diagram/table/chart is accurate (as applicable).

*Goes beyond requirements of problem.

Level 2 Satisfactory *Shows understanding of concepts.


*Computation is mostly correct.

*Written explanation is effective.

*Diagram/table/chart is mostly accurate (as applicable).

*Satisfies all requirements of problem.

Level 1 Nearly Satisfactory *Shows understanding of most concepts.

*May not use appropriate strategies.


*Written explanation is satisfactory.


*Satisfies most of the requirements of problem.

Level 0 Unsatisfactory *Shows little or no understanding of the concept.


*Computation is incorrect.

*Written explanation is not satisfactory.

*Diagram/table/chart is not accurate (as applicable).

*Does not satisfy requirements of problem.


OBJ: 4-1.4 Solve problems and show solutions.

NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3 | NA 8


TOP: Solve problems and show solutions.

KEY: Problem Solving | Show Solutions

2. A musician’s fan club had 35,000 members in 1999 and grew to 99,000 members by 2004.

Fan club membership

Nu

mb

er o

f m

emb

ers

(in

th

ou

san

ds)

(1999, 35,000)

(2004, 99,000)

1998 1999 2000 2001 2002 2003 2004 x

200

300

400

500

600

700

800

900

1000

1100

y

Year

a. Explain how the slope-intercept form can be used to predict the number of members in 2007.

b. Discuss how slope-intercept form is used in linear extrapolation.

ANS:

Sample answer:

a. You can use the slope-intercept form of the equation to find the y-value for any requested x-value.

The number of members in the fan club in 2007 will be 137,400.

b. Linear extrapolation is when you use a linear equation to predict values that are outside of the given

points on the graph.




Linear extrapolation is using a linear equation to predict values that are beyond the range of the data.

Assessment Rubric



























NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 3 | NA 4

STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c



3. Megan wants to change her Internet Service Provider. She is considering three different plans.

Plan 1 charges a $15 monthly fee plus $0.08 per minute of use.

Plan 2 charges a $5 monthly fee plus $0.11 per minute of use.

Plan 3 charges a flat monthly fee of $49.95.

a. For each plan, write an equation that represents the monthly cost C for m minutes per month.

b. Graph each of the three equations on the same coordinate axes. Label each line.

c. Megan expects to use 500 minutes per month. In which plan do you think Megan should enroll?

Explain.

ANS:

Sample Answer

a. Plan 1:

Plan 2:

Plan 3:

b.

Plan1

Plan

2

Plan 3

50 100 150 200 250 300 350 400 450 500 m

5

10

15

20

25

30

35

40

45

50

55

60

C

c. Megan should enroll in Plan 3. The graph shows that at 500 minutes, she would be paying $49.95

for Plan 3, about $60 for Plan 2, and about $55 for Plan 1.

Assessment Rubric



























NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6

STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c TOP: Performance assessment


4. a. Illustrate how you can determine whether two lines are parallel or perpendicular.

b. Are the two lines graphed below parallel? Explain.

c. Write an equation with a graph perpendicular to the lines graphed. Explain.

O

y x= -(5/8) + (1/8)

y x= -(5/8) + 3

x

y

ANS:

a. Sample answer: If two equations have the same slope, then the lines are parallel. If the product of

their slopes equals –1, then the lines are perpendicular, except for horizontal and vertical lines.

b. Yes, the lines are parallel as the slopes are equal.

c. The graph of is perpendicular to the graph of and because the

slopes are negative reciprocals of each other.

Two nonvertical lines are parallel if they have the same slope.


Assessment Rubric



























NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 7 | NA 3




5.

Average Hourly Earnings (dollars) of U.S. Production Workers, 1991-2001

Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Earnings 10.32 10.57 10.83 11.12 11.43 11.82 12.28 12.78 13.24 13.76 14.32

Source: Bureau of Labor Statistics, U.S. Dept. of Labor

a. Draw a scatter plot with years on the x-axis and earnings on the y-axis.

b. Draw a line of fit for the data.

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

d. Predict the hourly earnings for production workers in 2005.

ANS:

Sample Answer

a. and b.

Average Hourly Earnings (dollars) of U.S.

Production Workers, 1991-2001

1990 1992 1994 1996 1998 2000 2002 2004 x

10

11

12

13

14

15

16

y

Year

c. Using (1992, 10.57) and (2000, 13.76), the slope of the line is: .

Find b using one of the points.

The equation for the line of fit is

d.

Hourly earnings in 2005 should be about $15.76.

Assessment Rubric



















Level 0 Unsatisfactory

*Shows little or no understanding of the concept.








NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 | NA 3


TOP: Performance assessment KEY: Problem Solving | Show Solutions

6. Alan used his graphing calculator to find the best-fit line of a set of data. The correlation coefficient

was -0.965. Explain what that means.

ANS:

The correlation coefficient measures the how closely the best-fit line is modeling the data. The closer it

is to 1 or -1, the more closely it models the data. The best-fit line is a good model for the data because

-0.965 is very close to -1. The fact that it is negative means that there is a negative correlation.

Assessment Rubric


























OBJ: 4-6.3 Solve problems and show solutions. STA: OK 3.1c

TOP: Regression and median fit lines.

KEY: linear regression | best-fit line | correlation coefficient

7. Is a function? Explain.

ANS:

No it is not a function. A function has to have a unique y value for every x value. If x is 2, y would be

either or .

Assessment Rubric


























OBJ: 4-7.3 Solve problems and show solutions. TOP: Special functions.

chapter 4: linear functions and relations · obj: 4-1.1 write and graph linear equations in...

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