Question

Assume that $y$ varies inversely as $x$, how do you write an inverse variation equation that relates $x$ and $y$ given $y=-4$ when $x=16$?

Answer 1

Write an inverse variation equation:

The variable $y$ varies inversely as $x$.

$y\propto \frac{1}{x}$

The relationship between $x$ and $y$ can be expressed as,

$y=\frac{k}{x}...\left(1\right)$

Where, $k$ is proportionality constant.

Substitute the values in the equation.

$\begin{array}{rcl}-4& =& \frac{k}{16}\\ \therefore k& =& -64\end{array}$

Substitute the value in the equation $\left(1\right)$.

$y=-\frac{64}{x}$

Hence, the inverse variation equation that relates $x$ and $y$ is $\mathit{y}\mathbf{=}\mathbf{-}\frac{\mathbf{64}}{\mathbf{x}}$.