Question

Is `7x+4y=2` a direct variation equation and if so, what is the constant of variation?

Answer 1

It is a direct variation is you can rewrite it in the form `y=m*x` where `m` is the constant.

Explanation:

We first bring the `y`'s to one side and the rest to the other, by subtracting `7x` from both sides:
`4y=-7x+2`

Then divide both sides by 4:
`y=-7/4x+1/2`

This is a linear equation, but according to my definition, this is not a direct variation, as there is allways this constant `1/2`. The graph of a direct variation should go through the origin:
graph{7/4x+1/2 [-10, 10, -5, 5]}