# How do you find the variation constant and an equation of variation where y varies inversely as x and y=9 when x =12?

Dec 3, 2016

The equation is $y = \frac{108}{x}$ where $108$ is the constant of variation.

#### Explanation:

If y varies inversely with x, the equation is $y = \frac{k}{x}$, where $k$ is a constant.

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

To find $k$, substitute in $y = 9$ and $x = 12$..

$9 = \frac{k}{12}$

$\frac{9}{1} = \frac{k}{12} \textcolor{w h i t e}{a a a}$Rewrite $9$ as $\frac{9}{1}$

$1 \cdot k = 9 \cdot 12 \textcolor{w h i t e}{a a a}$Cross multiply

$k = 108$

Thus, the equation of variation is

$y = \frac{108}{x}$ where $108$ is the constant of variation.