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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