# How do you write an inverse variation equations given y = 8 when x = 4?

Jan 13, 2016

$x y = 32$
or
$y = \frac{32}{x}$

#### Explanation:

An inverse variation equation can be written in the form:
$\textcolor{w h i t e}{\text{XXX}} x y = c$ for some constant $c$

If $\left(x , y\right) = \left(4 , 8\right)$ is a solution pair for this equation:
$\textcolor{w h i t e}{\text{XXX}} \left(4\right) \cdot \left(8\right) = c$

$\Rightarrow c = 32$