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If y varies directly with x, and if y = 2/3 when x = 1/4, how do you find the direct variation equation?

1 Answer

Apr 6, 2016

$3 y = 8 x$ $3y=8x$

Explanation:

If $y$ $y$ varies directly with $x$ $x$ then
$XXX y = c \cdot x$ $color(white)("XXX")y=c*x$ for some constant of variation $c$ $c$

If $(x, y) = (\frac{1}{4}, \frac{2}{3})$ $(x,y)=(1/4,2/3)$ is a solution to this equation, then
$XXX \frac{2}{3} = c \cdot \frac{1}{4}$ $color(white)("XXX")2/3 = c*1/4$

$XXX \to c = \frac{2}{3} \cdot \frac{4}{1} = \frac{8}{3}$ $color(white)("XXX")rarr c=2/3 *4/1 = 8/3$

So
$XXX y = \frac{8}{3} x$ $color(white)("XXX")y=8/3x$
or (clearing the fraction)
$XXX 3 y = 8 x$ $color(white)("XXX")3y=8x$

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