Question

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

Answer 1

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]}