Question

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

Answer 1

`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.