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

1 Answer
Alan P.
Nov 7, 2015

direct variation equation:
eithercolor(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
eithercolor(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
thencolor(white)("XXX")(-16)/x = 2/3
rarrcolor(white)("XXX")x=(-16)*(3/2) =-24

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