Question

How do you write the direct variation equation if y=12 when x=18, find x when y=-16?

Answer 1

direct variation equation:
either`color(white)("XXX")y/x = 2/3color(white)("XXX")orcolor(white)("XXX")y = 2/3x`

If `y=-16` then `x=-24`

Explanation:

(There seems to be some local disagreement on standard form for a direct variation equation).

For a direct variation equation in variables `x` and `y` the default is that `y` is the dependent variable, so the form is
either`color(white)("XXX")y/x=c color(white)("XXX")orcolor(white)("XXX")y=c*x`
`color(white)("XXXXXXXXX")`for some constant `c`

Given that `(x,y) =(18,12)` is a solution for this equation
`color(white)("XXX")c= y/x = 12/18 = 2/3`

So the equation could be written as
`color(white)("XXX")y/x=2/3`

If `y=-16`
then`color(white)("XXX")(-16)/x = 2/3`
`rarrcolor(white)("XXX")x=(-16)*(3/2) =-24`