1. 11-3: Direct and Inverse Variation
Models for Direct and Inverse Variation
Direct Variation
Inverse Variation y y x x
x and y vary directly if for a constant k
x and y vary inversely if for a constant k or or
“division”
“in line”

2. k is a constant of variation
Ex 1: When x = 3, y = 12. Find an equation that relates x and y in each case.
a.) x and y vary directly.
“division”
1.) Find k.
2.) Write an equation. or

3. Ex 1: When x = 3, y = 12. Find an equation that relates x and y in each case.
b.) x and y vary inversely.
“in line”
1.) Find k.
2.) Write an equation. or

4. Ex 2: When x = 2, y = 4. Find an equation that relates x and y in each case.
a.) x and y vary directly.
“division”
1.) Find k.
2.) Write an equation. or

5. Ex 2: When x = 2, y = 4. Find an equation that relates x and y in each case.
b.) x and y inversely.
“in line”
1.) Find k.
2.) Write an equation. or

6. x 1 2 3 4 y 12 6 4 3 Inverse variation y x
Ex 3: Decide if the data shows direct or inverse variation.
Write an equation. x y
Inverse variation y x

7. Ex 4: Decide if the data shows direct or inverse variation.
Write an equation. x y
Direct Variation y x

8. inverse variation direct variation
Ex 5: State whether the variables have direct variation or inverse variation.
1.) The area B of the base and the height H of a prism with a volume of
10 cubic units are related by the equation BH = 10.
inverse variation
2.) The velocity v of a falling object and the time t it has fallen are
related by the equation 32t = v.
consider
direct variation