Objective- To use and write equations involving direct variation

Direct Variation- When a dependent variable y is proportional to and varies directly with an independent variable x.

y = k x k = constant of variation (any non-zero real number)

Circle the examples of direct variation.

y 4x

y x

2y 5x

y x

y7

x

3y x

yx

3

2y x

3

3 3

The variable y varies directly with x. Whenx = 3, y = 21. Find the value of y when x = 8.

y = k x

21 k 3

7 k

y = 7 x

y 7 8

y 56

It takes 5 cups of flour to bake 65 cookies.How many cookies can be made with 7 cupsof flour?

Let x = cups of flourLet y = # of cookies

5 5

y = k x

65 k 5

13 k

y = 13 x

y 13 7

y 91 cookies

Graph a Direct Variation1

Graph y x2

x y-3-2-1 0 1 2 3 4

-1.5-1-0.5

00.51

1.52

x

y

x x

Use Data to Write a Direct Variation

Pinky

Forefinger

(x)

(y)

5.4 6.8 7.5 8.1 cm

6.5 8 9 9.8 cmy

kx

1.20 1.18 1.2 1.21

Write a direct variation equation that relates the length of a person’s forefinger to their pinky.

Let y = forefinger lengthLet x = pinky length

y kx

k 1.20y 1.2x