Lesson 2.7 Skills Practice - Breal

Lesson 2.7 Skills Practice

Name_________________________________________________________ Date__________________________

Connecting Representations of Proportional Relationships

Interpreting Multiple Representations of Direct Proportions

Problem Set

Determine whether the relationship is directly proportional. Explain your reasoning. 1. The table shows the relationship between the numbers of hours that a plumber works on a job and the amount the plumber charges for the job.

Number of Hours

Amount Charged (dollars)

3

$220

5

$340

6

$400

________________ I set up the ratio na ummobunert cohf ahrogu erdsfor each pair of values. ____ __ ____ ____ __ 2 2305 7331 34505 6846005 6632

The ratios are not constant, so the relationship between the number of hours and the amount charged is not directly proportional.

2. The equation c 5 0.45p shows the relationship between the cost (c) of printing a yearbook and the number of pages ( p) in the book. The equation is in the form y 5 kx, with k 5 0.45, so the relationship is directly proportional.

? 2011 Carnegie Learning

Chapter 2 Skills Practice ? 427

Lesson 2.7 Skills Practice

page 2

3. The table shows the relationship between the size of a painting and the cost of the painting.

Size (square centimeters)

Cost (dollars)

240

$7.20

610

$18.30

900

$27.00

_____ I set up the ratio cs oizsetfor each pair of values. _____ ______ 72.42005 0.031681.3005 0.03_2_97_0._00_0_5 0.03

The ratios are constant, so the relationship between the size of a painting and the cost of the painting is directly proportional.

4. Emilio bought _1_pound of raisins for $1.07, while Tory bought 1_1_pounds of raisins for $3.21.

2

2

________ I set up the ratio p ocuonsdtsfor each pair of values.

_____ _____ 10.0.575 2.1431..2515 2.14

The ratios are constant, so the relationship between the cost and the number of pounds of raisins is directly proportional.

? 2011 Carnegie Learning

428 ? Chapter 2 Skills Practice

Lesson 2.7 Skills Practice

page 3

Name_________________________________________________________ Date__________________________

5. The graph shows the relationship between the age of a cat and its corresponding age in "human years."

Human Years

y

The points form a straight line, but

100

the line does not go through the origin.

90

Therefore, the relationship is not directly

80

proportional.

70

60

50

40

30

20

10

x 2 4 6 8 10 12 14 16 18 20

Cat Years

6. The graph shows the relationship between the number of clowns and number of jugglers needed for a performance.

y

The points form a straight line, the

20 18 16

__ points go through (0, 0), and any two

points on the graph have a ratio 41 . Therefore, the relationship is directly

14

proportional.

12

10

8

6

4

2

x 2 4 6 8 10 12 14 16 18 20

Number of Clowns

? 2011 Carnegie Learning Number of Jugglers

Chapter 2 Skills Practice ? 429

Lesson 2.7 Skills Practice

page 4

Determine the constant of proportionality and interpret it in the context of each problem.

7. The distance (d) Mr. Benson can drive is directly proportional to the number of gallons (g) of gas in his car. He needs 15 gallons of gas to drive 480 miles. The equation for the relationship is d 5 32g, so k 5 32. It is the number of miles Mr. Benson can drive on 1 gallon of gas.

8.The table shows the relationship between the number of minutes customers use the Internet at an Internet caf? and the amount they are charged for using it.

Number of Minutes

Cost (dollars)

8

$1.20

15

$2.25

40

$6.00

________ I set up the ratio m cinousttesfor a pair of values, _6 _4._00_0_5 0.15, so k 5 0.15. It is the cost

per minute for using the Internet.

9. The equation t 5 25p shows the relationship between the time (t) to deliver newspapers in seconds and the number of papers (p) delivered. The equation is in the form y 5 kx, with k 5 25. It is the number of seconds it takes to deliver 1 newspaper.

? 2011 Carnegie Learning

430 ? Chapter 2 Skills Practice

Lesson 2.7 Skills Practice

page 5

Name_________________________________________________________ Date__________________________

10. The graph shows the relationship between the number of tickets Ricky buys and the number of rides he can ride.

y 9

_______ I set up the ratio tircidkeestsfor a pair of values, ___ __ __ 1225 61 , so k 5 61 . Each ride requires

8

6 tickets.

7

Number of Rides

6

5

4

3

2

1

x 3 6 9 12 15 18 21 24 27 30

Number of Tickets

11. The equation a 5 _14_5_m shows the relationship between the number of advertisements (a) during a television program and the number of minutes (m) the program lasts.

___ The equation is in the form y 5 kx, with k 5 145. There are 4 advertisements for every 15 minutes

of the television program.

12. The number of buttons (b) Sally needs to make shirts for a dance team is directly proportional to the number of shirts (s) she needs to make. She needs 36 buttons to make 3 shirts. The equation for the relationship is b 5 12s, so k 5 12. It is the number of buttons she needs for each shirt.

? 2011 Carnegie Learning

Chapter 2 Skills Practice ? 431

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download