Question

If y varies directly with x and y = -4 when x = 12.5, how do you find y when x = 24?

Answer 1

`y=-7.68`

Explanation:

A direct variation can be written as `y=kx`. Since we are given a matched `x` and `y` value, we can first compute for the constant of variation `k`.

`y=kx`
`(-4)=k(12.5)`
`(1/12.5)(-4)=(1/cancel12.5)k(cancel12.5)`
`-4/12.5=k`
`color(blue)(k=-0.32)`

Now that we know the constant of variation, we can now solve for the value of `y` when `x=24`.

`y=color(blue)(k)x`
`y=color(blue)((-0.32))x`
`y=color(blue)((-0.32))(24)`
`color(red)(y=-7.68)`