# How do you find "k" if y varies inversely as x and if y=24 when x=3?

Apr 6, 2018

$k = 72$

#### Explanation:

Recall that the general form for inverse variation models is $y = \frac{k}{x}$. You may also write it as $x y = k$, which more clearly explains the name "inverse". When $x$ is multiplied by some value, $y$ must be divided by the same value, and vice-versa.

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

$\left(\textcolor{red}{3} , \textcolor{red}{24}\right)$ lies on the curve. The equation must hold true for $\textcolor{red}{x = 3}$ and $\textcolor{red}{y} = 24$.

$\textcolor{red}{24} = \frac{k}{\textcolor{red}{3}}$

And isolating $k$:

$72 = k$