Question

If $y$varies inversely with$x$and$y=5$when$x=4$, find the equation that relates$x$and$y$.

Short answer

The equation relating $x$and $y$is $x=\frac{20}{y}$.

Step-by-step solution

Step 1. Given information

Given that $y$varies inversely as $x$and $y=5$when $x=4$.

Step 2. Determine the equation relating x and y.

As $y$varies inversely as $x$so, for some constant $k$, $y=\frac{k}{x}$.

Label the obtained equation.

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

Substitute the given values and solve for $k$.

localid="1645958114900" $\begin{array}{rcl}5& =& \frac{k}{4}\\ 20& =& k\end{array}$

Substitute 20 for $k$into equation $\left(1\right)$.

$x=\frac{20}{y}$