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

1 Answer
Johnson Z.
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)#.

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