# Assume y varies inversely as x, if y=5 when x=6, how do you find x when y=2?

Aug 17, 2017

15

#### Explanation:

If y varies inversely as x, the two variables can be represented in an equation in the form $y = \frac{k}{x}$ where $k$ is some constant.

We are given that $y = 5$ when $x = 6$. We can plug this into the above equation to find what $k$ is:

$5 = \frac{k}{6}$
$30 = k$

Based on this we can create our equation:

$y = \frac{30}{x}$

And then find $x$ when $y = 2$:

$2 = \frac{30}{x}$
$2 x = 30$
$x = 15$