1. Direct Variation

2. Objectives To learn what direct variation is
To solve problems using direct variation
To solve real-life problems using direct variation

3. What is Direct Variation?
Direct variation means that in an equation, one term is multiplied by a constant to get the other term.
If k is the constant, the formula is written y = kx.
For example, in the equation y = 4x, 4 is the constant. If x is 2, y is 8. If x is -6, y is -24.

4. What is Direct Variation?
Direct variation also means that the variables are proportional.
Example: Y varies directly with x. When x is 4 y is 20, when y is -10, what is x?
-40=20x
x = -2 x
-10

5. Direct Variation Examples
Y varies directly with x. When x is 3, y is When x is 7, what is y?
H varies directly with p. When h is 9, p is 13. When p is 8, what is h? 7
3y = 73.5
y = 24.5 y h
13h = 72
h ≈ ? 8

6. Direct Variation Examples
X varies directly with Y. When x is 42, y is -6. When x is 21, what is y?
w varies directly with x. When w is 2, x is 28. When w is 7, what is x? 21
42y = -126
y = ? y 7
2x = 196
x = ? x

7. Direct Variation Word Problems
The shadow of an object varies directly with its height. The shadow of a 25 ft object is 6 ft. How long is the shadow of an 18 ft tree? 18
25s = 108
s = 4.32 s
The shadow of the tree is 4.32 ft.

8. Direct Variation Word Problems
The circumference of a circle varies directly with the diameter. The diameter of a circle is 6 in and the circumference is in. If the circumference of a circle is 25 ft, what is the diameter to the nearest hundredth? d
150 = 18.84d
d = 7.96 25
The diameter is 7.96 ft.

9. Direct Variation Word Problems
The number of potatoes harvested varies directly with the area of the garden. If 200 potatoes are harvested from 10 square feet, how many potatoes would be harvested from 45 square feet? p
9000 = 10p
p = 900 45
900 potatoes could be harvest in 45 ft2.