1. 3.8 – Direct, Inverse, and Joint Variation

2. Direct Variation When two variables are related in such a way that the ratio of their values remains constant. “y varies directly as x” would simply mean as x increases – so does y. Or as x decreases – so does y. Form: y = kx n ; n > 0, k is nonzero k is called the constant of variation.

3. The variables x and y vary directly and y=15 when x=3. a) Write the equation relating x and y. b) Find y when x = 9.

4. The y varies directly as the cube of x and y=-67.5 when x=3. a) Write the equation relating x and y. b) Find x when y = -540.

5. Inverse Variation When the values of two quantities are related inversely proportional. As one value increases, the other value decreases and vice versa y = k/x n or x n y= k, n > 0

6. The variables x and y vary inversely when y = 14 when x = 3. a) Write the equation relating x and y. b) Find y when x = 9.

7. Suppose y varies inversely with x 2. When y = 15, x = 2. a) Write the equation relating x and y. b) Find y when x = 5.

8. Joint Variation A variation when one or more quantities vary directly as the product of two or more other quantities. y = kx n z n ; x and z are nonzero and n > 0

9. Example 1 If y varies jointly as x and the cube of z and y = 16 when x = 4 and z = 2, find y when x = -8 and z = -3

10. Example 2 If y varies jointly as x and z and inversely as the square of w, and y = 3 when x = 3, z = 10, and w = 2, find y when x = 4, z = 20, and w = 4.

11. Homework 3.8 page 194 # 15, 18, 20