How to find inverse variation

To solve for an inverse, we switch x and y and solve for y. Doing so yields:

Because we know and vary inversely, we know that for some .

When , . .

When , . .

Therefore, when , we have so

1. Switch the and variables in the above equation.

2. Solve for :

If varies inversely with , .

1. Using any of the two combinations given, solve for :

Using :

2. Use your new equation and solve when :

An inverse variation is a function in the form: or , where is not equal to 0.

Substitute each in .

Therefore, the constant of variation, , must equal 24. If varies inversely as , must equal 24. Solve for .