Lesson 5 Skills Practice - 8TH GRADE MATH DEPARTMENT

[Pages:4]NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Lesson 5 Skills Practice

Direct Variation

For Exercises 1?4, determine whether each linear function is a direct variation. If so, determine the constant of variation. If not, explain why not.

1.

Volume, x

2

4

6

8

Mass, y

10

20

30

40

2.

Gallons, x

5

10

15

20

Miles, y

95 190 285 380

3.

Time, x

8

9

10 11

Temperature, y 68 71 74 77

4.

Age, x Height, y

3

6

28

40

9

12

52

64

For Exercises 5?8, y varies directly with x. Write an equation for the direct variation. Then determine each value.

5. If y = 27 when x = 8, determine y when x = 11.

6. Determine y when x = 12, if y = 2 when x = 5.

7. Determine y when x = 3, if y = ?4 when x = ?9.

8. If y = 20 when x = 8, what is the value of x when y = ?2?

Course 3 ? Chapter 3 Proportional Relationships and Slope

NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Lesson 5 Homework Practice

Direct Variation

For Exercises 1?2, determine whether each linear function is a direct variation. If so, determine the constant of variation. If not, explain why not.

1.

Price, x Tax, y

$5 $10 $15 $20 $0.41 $0.82 $1.23 $1.64

2.

Age, x

8

9

10

11

Grade, y

3

4

5

6

For Exercises 3?5, y varies directly with x. Write an equation for the direct variation. Then determine each value. 3. If y = 12 when x = 6, determine y when x = 18.

4. If y = 8 when x = 3, determine y when x = 45.

5. If y = ?4 when x = 10, determine y when x = 2.

6. The number of sticks of gum varies directly as the number of packages. There are 36 sticks of gum in 2 packages. Suppose you have 5 packages of gum. Write and solve a direct variation equation to determine how many sticks you have?

7. The rental fee to rent jet skis varies directly as the number of hours that you rent them. Fun Vacation Rentals rents jet skis to tourists. They charge $140 for 4 hours. Suppose you rent a jet ski for only 3 hours. Write and solve a direct variation equation to determine your rental fee?

8. The amount Ben earns y varies directly with the number of hours he works x as shown in the graph. Write a direct variation equation. Identify the constant of variation and interpret its meaning.

Course 3 ? Chapter 3 Proportional Relationships and Slope

NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Lesson 5 Problem-Solving Practice

Direct Variation

1. The amount Gadin Carpets earns varies directly with the number of carpets cleaned. How much does the company earn for each carpet it cleans?

2. The number of cars built varies directly as the number of hours the production line operates. What is the ratio of cars built to hours of production?

3. A car drives 283.5 miles in 4.5 hours. Assuming that the distance traveled varies directly with the time traveled, how far will the car travel in 7 hours?

4. The number of kilograms that an object weighs varies directly as the number of pounds. If an object weighs 45 kilograms or about 100 pounds, about how many kilograms is an object that weighs 70 pounds?

5. The amount of cable that is wound on a spool varies directly with the amount of time that passes. Determine the speed at which the cable moves.

6. A rectangle on a digital display board is made so that its width varies directly as its length. The current rectangle displayed is shown below. What is the area of a rectangle that is 15 inches long?

Course 3 ? Chapter 3 Proportional Relationships and Slope

NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Lesson 5 Extra Practice

Direct Variation

For Exercises 1?2, determine whether each linear function is a direct variation. If so, determine the constant of variation. If not, explain why not.

1.

Hours, x Distance, y(miles)

11 $0.41

12 $0.82

13 $1.23

14 $1.64

2.

Hours, x

5

8

11

14

Earnings, y 40

64

88 112

For Exercises 3?5, y varies directly with x. Write an equation for the direct variation. Then determine each value. 3. If y = 16 when x = 4, determine y when x = 9.

4. If y = ?5 when x = 2, determine y when x = 8.

5. If y = ?7 when x = ?21, determine x when y = 9.

6. Bruce rents snowmobiles to tourists. He charges $135 for 4 hours and $202.50 for 6 hours? What is the hourly rate Bruce charges to rent a snowmobile?

7. The power absorbed by a solar panel varies directly with its area. If an 8 square meter panel absorbs 8,160 watts of power, how much power does a 12 square meter solar panel absorb?

8. The amount Ramar saves y varies directly with the number of weeks he saves x as shown in the graph. Write a direct variation equation. Identify the constant of variation and interpret its meaning.

Course 3 ? Chapter 3 Proportional Relationships and Slope

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