# Suppose that x and y vary inversely, how do you write a function that models inverse variation given x=1 when y=11?

May 28, 2015

If $x$ and $y$ vary inversely, then

$x \cdot y = c$ for some constant $c$

If $\left(x , y\right) = \left(1 , 11\right)$ is a solution set for the desired inverse variation, then

$\left(1\right) \cdot \left(11\right) = c$

So the inverse variation is
$x y = 11$
or (in an alternate form)
$y = \frac{11}{x}$