Question

Is `-4x + y = 0` a direct variation and if so, how do you find the constant?

Answer 1

Yes. The constant is `4`.

Explanation:

We are given:

`-4x+y=0`

To vary directly means we can find a form `y = \alpha x`, where `\alpha` is some constant.

If we add `4x` to each side of the above equation we get:

`y = 4x`

So we can see that `y` and `x` vary directly by `4`.

Answer 2

#color(blue)(4)

Explanation:

Direct variation is given by:

`y=kx`

Where `k` is the constant of variation.

`-4x+y=0`

Rearrange to get y in terms of x:

`y=4x`

Compare:

`y=kx`
`y=4x`

So `-4x+y=0` does represent direct variation.

`:.`

Constant of variation is:

`k=color(blue)(4)`