Question

Is `3y - 7 = 10x` a direct variation equation?

Answer 1

No. In order to be a direct variation, the line must go through the origin, `(0,0)`.

Convert `3y-7=10x` to slope-intercept form.

`3y-7=10x`

Subtract 7 from both sides.

`3y=10x+7`

Divide both sides by 3.

`y=10/3x+7/3`

If `x=0`:

`y=10/3*0+7/3`

`y=7/3`

The point is `(0,7/3)`

So the line does not go through the origin.

graph{y=10/3x+7/3 [-10, 10, -5, 5]}