# If y varies inversely as x, how do you find the constant of variation if y=36 when x=9?

Feb 5, 2015

In inverse proportions the rule is that $x \cdot y = C$ where $C$ is a constant.

In your case $C = 9 \cdot 36 = 324$

Let's do a few examples:

We double $x$, then $y$ should be halved :
$x = 18 , y = 18 \to x . y = 18 \cdot 18 = 324$ as expected

We divide $x$ by 3, then $y$ should be times 3
$x = 9 / 3 = 3 , y = 3 \cdot 36 = 108 \to x \cdot y = 324$

That's really all there is to it.

So for any $x \ne 0$, then $y = 324 / x$
Here's a graph (you'd probably only use the positive side)
graph{324/x [-213.8, 213.7, -106.8, 107]}