# How do you write an inverse variation equation that relates x and y when you assume that y varies inversely as x given that if y=124 when x=12, find y when x= -24?

May 26, 2015

An inverse variation has the form
$y = \frac{c}{x}$ for some constant $c$

Given $\left(x , y\right) = \left(12 , 124\right)$ is a solution pair for the desired inverse variation:
$124 = \frac{c}{12}$
$\rightarrow c = 1488$
and the inverse variation equation is
$y = \frac{1488}{x}$

When $x = - 24$ this becomes
$y = \frac{1488}{- 24} = - 62$