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

2 Answers
Alan P.
Jan 2, 2018

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

Explanation:

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

Jim G.
Jan 2, 2018

k=-2k=−2

Explanation:

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

•color(white)(x)y=kxlarrcolor(blue)"k is the constant of variation"∙xy=kx←k is the constant of variation

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

"divide both sides by 6"divide both sides by 6

y=-2xlarrcolor(blue)"direct variation equation"y=−2x←direct variation equation

"with "k=-2with k=−2

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