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

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

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Answer 1 · 2015-11-07T11:49:38

direct variation equation:
either $XXX \frac{y}{x} = \frac{2}{3} XXX or XXX y = \frac{2}{3} x$ $color(white)("XXX")y/x = 2/3color(white)("XXX")orcolor(white)("XXX")y = 2/3x$

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

Explanation:

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

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

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

So the equation could be written as
$XXX \frac{y}{x} = \frac{2}{3}$ $color(white)("XXX")y/x=2/3$

If $y = - 16$ $y=-16$
then $XXX \frac{- 16}{x} = \frac{2}{3}$ $color(white)("XXX")(-16)/x = 2/3$
$\to XXX x = (- 16) \cdot (\frac{3}{2}) = - 24$ $rarrcolor(white)("XXX")x=(-16)*(3/2) =-24$

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

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