Question

Is `8x +2y =0` a direct variation equation and if so what is the constant?

Answer 1

Yes, the equation represents direct variation. The constant is `-4`.

Explanation:

In order to determine whether or not the given equation exhibits direct variation, you must first isolate for `y` such that the equation is rewritten in slope-intercept form, which is `y=mx+b`.

Thus,

`8x+2y=0`

`2y=-8x`

`y=-4x`

Recall that the equation is technically,

`y=color(blue)(-4)xcolor(white)(i)color(red)(+0)`

In your case, since `color(red)(b=0)`, the equation does represent direct variation. Direct variation only occurs when the y-intercept is `0`.

Furthermore, the constant is the value of `color(blue)m`, which is `color(blue)(-4)`.