Lesson 8-4: Direct, Joint, and Inverse Variation

Direct Variation

y varies directly as x if there is a nonzero constant, k, such that y = kx*k is called the constant of variation

1. Plug in the two values you have and solve for the missing variable

2. Plug in that variable and the other given value to solve for the requested answer

Example

If y varies directly as x and y = 12 when

x = -3, find y when x = 16.

Joint Variation

y varies jointly as x and z if there is a nonzero constant, k, such that y = kxz

* Follow the same directions as before

Example

Suppose y varies jointly as x and z. Find y when x = 8 and z = 3, if y = 16 when z = 2 and x = 5.

Inverse Variation

y varies inversely as x if there is a nonzero constant, k, such that xy = k or y=

kx

Example

If y varies inversely as x and y = 18 when x = -3, find y when x = -11