Question

Is `3x + 4y = 0` a direct variation equation and if so, what is the constant of variation?

Answer 1

`3x+4y=0` is a direct variance equation
and its constant of variation is `(-3/4)`

Explanation:

A direct variance function will either be in or can be manipulated to be in the form:
`color(white)("XXX")y=m*x` for some constant `m`, the"constant of variation"

`3x+4y=0`

`rarr 4y=-3x`

`rarr y = (-3/4)x`

Another way to look at it:
If the equation is a straight line which is
`color(white)("XXX")`neither vertical nor horizontal
and
`color(white)("XXX")`passes through the origin `(0,0)`
then it is a direct variation.

Graph of `3x+4y=0`
graph{3x+4y=0 [-10, 10, -5, 5]}