# ACT Math : How to find inverse variation

## Example Questions

### Example Question #1 : How To Find Inverse Variation

Find the inverse equation of:

Explanation:

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

### Example Question #1 : How To Find Inverse Variation

Find the inverse equation of  .

Explanation:

1. Switch the  and  variables in the above equation.

2. Solve for :

### Example Question #3 : How To Find Inverse Variation

When ,  .

When .

If  varies inversely with , what is the value of  when ?

Explanation:

If  varies inversely with .

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

Using :

2. Use your new equation  and solve when :

### Example Question #1 : How To Find Inverse Variation

 x y

If  varies inversely with , what is the value of ?

Explanation:

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 .

### Example Question #1 : How To Find Inverse Variation

Two numbers  and  vary inversely, and  when . If this is true, what is the value of  when ?

Explanation:

If  when , and the variation is direct, then . Using this, we know that if .