Name ____________________________ Date _________________Math 7 Direct Variation

When two variable quantities have a constant ratio, their relationship is called a direct variation or a direct proportion. The constant ratio is called the constant of variation.

EX: Pizzas cost $8 each plus a $3 delivery charge. The table below shows the cost of 1,2,3, and 4 pizzas. Is there a constant rate? A direct variation?

9.5,

273 or 9,

354 or 8.75

Because there is no constant rate, there is no direct variation.

Determine whether each linear function is a direct variation. If so, state the constant of variation.

1.

Time, x 1 2 3Wages, y 12 24 36

_____________________

2.

Time, x 2 3 4Temperature, y 4 5 7

_____________________

3.

Year, x 5 10 15Height, y 12.5 25 37.5

_____________________

Number of Pizzas

1 2 3 4

Cost ($) $11 $19 $27 $35

The constant rate of change (constant of proportionality) is assigned a special variable, k.

To determine the constant of proportionality, k, from a graph and interpret it in the context of each problem

choose a point on the graph and express it as a ratio as follows: .

Symbols ory=kx , wherek¿0

* A direct variation graph will always be a straight line that goes through the origin.

EX: The height of the water as a pool is being filled is shown in the graph. Determine the constant of variation and interpret its meaning.

To determine the constant of variation, k, pick a point from the graph and write it as

25∨ 4

10∨0.4 Therefore, the pool fills up at a rate of .4 inch every minute.

(note that this is also the unit rate!)

4.) The graph below represents the price of bananas at one store. What is the constant of proportionality and explain what this means.

5.) Veronica is mulching her front yard. The total weight of mulch varies directly with the number of bags of mulch. What is the constant of proportionality and explain what this means. How much would 10 bags of mulch weigh?

6.) The money Steven earns varies directly with the number of dogs he walks. What is the constant of proportionality and explain what this means. How much money would he earn if he walked 20 dogs?

7.) BAKING The number of cups of flour varies directly as the number of rolls made. Four cups of flour are needed to make 24 rolls. How much flour is needed for 36 rolls? __________________________

8.) WEDDING FAVORS Lucius is making favors for his sister's wedding. If supplies for 25 favors cost $62.50, how much do supplies for 60 favors cost? __________________________

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

2.) 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