# Suppose y varies inversely as x. If y = 2 when x = 14, how do you find y when x = 7?

May 31, 2016

$y = 4$

#### Explanation:

Inverse Variation uses the equation $y = \frac{k}{x}$

Where $k$ is the constant of variation.

For this problem we will use the $y$ and $x$ to solve for the $k$, constant of variation.

$y = 2$
$x = 14$

$2 = \frac{k}{14}$

$14 \left(2\right) = \frac{k}{\cancel{14}} \left(\cancel{14}\right)$

$k = 28$

Now we solve for the $y$ when the $x$ is $7$

$y = \frac{28}{7}$

$y = 4$