Question

How do you determine whether the equation `-12x=6y` represents direct variation. If it does, how do you find the constant of variation?

Answer 1

If an expression can be re-formatted into the form:
`color(white)("XXX")y=color(blue)c * x` for some constant `color(blue)c` then it is a direct variation.

Explanation:

In this case `-12x=6y`
can be written as
`color(white)("XXX")y=color(blue)(""(-2))x`
and therefore it is a direct variation.

Answer 2

`k=-2`

Explanation:

`"the equation for direct variation is of the form"`

`•color(white)(x)y=kxlarrcolor(blue)"k is the constant of variation"`

`6y=-12x" can be expressed as"`

`"divide both sides by 6"`

`y=-2xlarrcolor(blue)"direct variation equation"`

`"with "k=-2`