# Suppose y varies inversely with x, how do you write an equation for the inverse variation if y = 9 when x = 4?

May 26, 2015

If $y$ varies inversely with $x$
then
$y = \frac{c}{x}$ for some constant $c$

Given that $\left(x , y\right) = \left(4 , 9\right)$ is a solution to this equation:
$9 = \frac{c}{4}$

$\rightarrow c = 36$

and the equation is
$y = \frac{36}{x}$