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

1 Answer
Feb 5, 2015

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]}