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

1 Answer
May 5, 2016

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).