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

1 Answer
Dec 14, 2015

#y=-8x# is a direct variation with variation constant #=(-8)#

Explanation:

Any equation of the form
#color(white)("XXX")y/x=c# or #y=c*x# is a direct variation equation with constant #c#

Note that the constant does not need to be #> 0# (in case that was causing confusion).

Another way to look at it:
Any linear equation that passes through the origin is a direct variation (the constant of variation is the slope of the line).
So both of the lines below are direct variations:
graph{(y+3x)*(2y-x)=0 [-10, 10, -5, 5]}

But neither of the following are direct variations:
graph{(x^3) [-8.89, 8.9, -4.444, 4.445]}
Not "linear"

graph{4x+3 [-8.89, 8.9, -4.444, 4.445]}
Does not pass through the origin.