Question

How do you find "k" if y varies inversely as x and if `y=24` when `x=3`?

Answer 1

`k = 72`

Explanation:

Recall that the general form for inverse variation models is `y = k/x`. You may also write it as `xy = k`, which more clearly explains the name "inverse". When `x` is multiplied by some value, `y` must be divided by the same value, and vice-versa.

`y = k/x`

`(color(red)3, color(red)24)` lies on the curve. The equation must hold true for `color(red)(x = 3)` and `color(red)y = 24`.

`color(red)24 = k/color(red)3`

And isolating `k`:

`72 = k`