# If x varies inversely with y and x = 8 when y = 10, how do you find y when x = 6?

Jun 16, 2016

$y = \frac{40}{3} \mathmr{and} 13 \frac{1}{3}$

#### Explanation:

This is an example of inverse proportion, or inverse variation.

To change a proportion into an equation, multiply by a constant and then use the values given to find the value of the constant.
$y \propto \frac{1}{x}$

$y = \frac{k}{x} \Rightarrow k = x y$

$k = 8 \times 10 = 80$

So, $y = \frac{80}{x}$

When $x = 6 , \text{ } y = \frac{80}{6}$

$y = \frac{40}{3} \mathmr{and} 13 \frac{1}{3}$