How do you find the variation constant and an equation of variation where y varies inversely as x and y=9 when x =12?

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Answer 1 · 2016-12-03T00:29:49

The equation is $y = \frac{108}{x}$ $y=108/x$ where $108$ $108$ is the constant of variation.

If y varies inversely with x, the equation is $y = \frac{k}{x}$ $y=k/x$ , where $k$ $k$ is a constant.

$y = \frac{k}{x}$ $y=k/x$

To find $k$ $k$ , substitute in $y = 9$ $y=9$ and $x = 12$ $x=12$ ..

$9 = \frac{k}{12}$ $9=k/12$

$\frac{9}{1} = \frac{k}{12} a a a$ $9/1=k/12color(white)(aaa)$ Rewrite $9$ $9$ as $\frac{9}{1}$ $9/1$

$1 \cdot k = 9 \cdot 12 a a a$ $1*k=9*12color(white)(aaa)$ Cross multiply

$k = 108$ $k=108$

Thus, the equation of variation is

$y = \frac{108}{x}$ $y=108/x$ where $108$ $108$ is the constant of variation.