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

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Answer 1 · 2015-02-05T10:21:46

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

In your case $C=9*36=324$

Let's do a few examples:

We double $x$ , then $y$ should be halved :
$x=18,y=18->x.y=18*18=324$ as expected

We divide $x$ by 3, then $y$ should be times 3
$x=9//3=3, y=3*36=108->x*y=324$

That's really all there is to it.

So for any $x!=0$ , 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]}

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