Question

If y varies inversely with x, and y= 6 when x= 18, how do you find y when x= 8?

Answer 1

`y=13.5`

Explanation:

`y prop 1/x or y = k*1/x or x*y=k; y=6 ; x=18 :. 6*18=k or k=108` k= constant of variation. So the inverse variation equation is `x*y=108`
Now `x=8 :. 8*y=108 or y=108/8=13.5`[Ans]

Answer 2

`y = 13/5`

Explanation:

Inverse variations look like this: `y = k/x`

We need to make our own inverse variation given `y=6` and `x=18`. We can plug this into the standard inverse variation with variables.

`y = k/x`

`6 = k/18`

`108 = k`

We've determined that `k=108`. Now we have what it takes to create an inverse variation. This is our final equation:

`y = 108/x`

We still need to find what `y` equals when `x` is `8`. Let's plug in `8` for `x`.

`y = 108/x`

`y = 108/8`

`y = 13.5`