Name: Date: Period: REVIEW-Unit 7 Direct Variation
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1 Name: Date: Period: REVIEW-Unit 7 Direct Variation 1. The graph of similar triangles, JNL with vertices J( 3, 3), N( 3, 3), and L(5, 3) and KML with vertices K(1, 0), M(1, 3), and L(5, 3) is below. Write the correct proportion comparing the rise to the run for the similar slope triangles and its numeric value. 2. Determine whether the relationship between the two quantities shown in the table is linear. If so, determine the constant rate of change. If not, explain your reasoning. Distance Traveled on Bike Trip
2 3. The cost of 5 songs to download from itunes is $5.75. The cost of 8 songs is $9.20. The relationship between the number of downloaded songs and the cost is a proportional linear relationship. What is the cost per song s? 4. ABC is similar to MNC. What is the value of y? A (-4,2) (-2,y) M B (-4,-2) N (-2,-2) (4,-2) C 5. The value of y varies directly with x. Which equation represents the relationship between x and y, if y = 20 3 when x = 30? 6. The number of miles Madeline drove is directly proportional to the gallons of gasoline used. If the relationship between miles and gallons of gasoline can be represented by the equation, y = 30x, what is the unit rate? If x=5, what does y equal? If x=3, what does y equal?
3 7. Sandra earns $164 for working 16 hours. The amount of money Sandra earns is proportional to the number of hours she worked and can be represented by the equation, y = 10.25x. How long would it take Sandra to earn $512.50? 8. Amelia earned $40 for babysitting for 5 hours. The amount of money earned by Amelia while babysitting y and the number of hours spent babysitting x are in a proportional linear relationship. This situation can be represented by y = 8x. Graph the equation on a coordinate plane.
4 9. The table below shows the relationship between the cost of ground turkey at a local market and the number of pounds bought. Write an equation that represents the relationship of cost, y, to the number of pounds bought, x. 10. The number of walls Frank paints varies directly with the number of days he works. Frank paints 108 walls in 6 days. Suppose Frank works for 12 days. Write and solve a direct variation equation to find the number of walls Frank paints in 12 days. 11. 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.
5 12. A package of tennis balls contains 3 tennis balls. The number of tennis balls and the number of packages are in a proportional linear relationship. This situation can be modeled by y = 3x. Graph the equation. 13. The table shows that the number of gallons of water used to wash dishes in a dishwasher varies directly with the number of loads of dishes washed. How many gallons of water will be used to wash 13 loads of dishes?
6 14. The distance a spring stretches varies directly with the weight attached to the spring. If a spring stretches 9 inches with 100 pounds attached, how far will the spring stretch with 80 pounds attached? Round to the nearest tenth of an inch. 15. Luis drives at a rate of 50 miles per hour. His total distance in t hours is d. Write a direct variation equation that relates the variables. Then graph the equation.
7 16. 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. 17. The graph shows how the number of feet x relates to the corresponding number of yards y. Create a table that also represents the relationship? x y k = y x
8 18. Judy can decorate 3 cakes in 5 hours. Graph the direct variation of the number of cakes per hour that Judy can decorate. 19. The mass of a substance varies directly with the volume of the substance. The volume of 100 kilograms of the substance is 80 liters. What is the volume, in liters, of 3.2 kilograms of this substance? 20. The table below shows the relationship between the cost of mulch at a local garden store and the number of square feet bought. Write an equation that represents the relationship of cost, y, to the number of square feet bought, x.
November 30, direct variation ink.notebook. page 162. page Direct Variation. page 163. page 164 page 165
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