Question

Is `-x+2y=0` a direct variation equation and if so what is the constant?

Answer 1

`k` is `1/2` which is the constant of variation.

Explanation:

Direct Variation is in in the `y=kx`, where `k` is the constant of variation.

We need to solve for the `y` variable.

`-x+2y=0`

Add `x` to both sides

`2y=0+x`

`2y=x`

Divide by `2` to isolate `y`

`cancel2y/cancel2=x/2`

`y=1/2x`

`k` is `1/2` which is the constant of variation.

Answer 2

Yes, it is a direct variation equation, and the constant of variation is `1/2`.

Explanation:

The general form of a direct variation equation is `y = kx`, with k being the constant of variation.
`-x + 2y = 0` can be transformed to fit the correct form:
`-x + x + 2y = 0 + x`
`2y = x`
`(2y)/2 = x/2`
`y = 1/2x`
Therefore, it is a direct variation equation and `k = 1/2`.