Question

How do you write an equation of the direct variation that includes the point (–5, 17)?

Answer 1

#17x+5y=0color(white)("XXX") or some equivalent variation

Explanation:

A direct variation equation can be written in the form:
`color(white)("XXX")y=c * x` with variables `x` and `y` and a constant `c`

If `(x,y)=(-5,17)` is a point for such a direct variation equation,
then
`color(white)("XXX")17=c * (-5)`
which implies
`color(white)("XXX")c=-17/5`

So one possible form of this equation would be
`color(white)("XXX")y=(-17/5)x`

This isn't very pretty, so we could multiply both sides by `5`
to get
`color(white)("XXX")5y=-17x`

...or even better, we could convert this into standard form
by adding `17x` to both sides:
`color(white)("XXX")17x+5y=0`