Question

Assume that $y$varies inversely as $x$. If $y=5$when $x=-4$write an inverse variation equation that relates $x$and $y$.

Short answer

The equation that relates $x$and $y$is$xy=-20$.

Step-by-step solution

Step 1. State the concept of inverse variation. 

Relationship of the form $xy=k$ or $y=\frac{k}{x}$where $x,y\ne 0$ for some nonzero constant$k$ is known as inverse variation i.e.,$y$ varies inversely as $x$.

Step 2. Calculate the constant of variation, k. 

Since $y$varies inversely as $x$an inverse variation equation is given by $xy=k$so, substitute 5 for $y$, $-4$for $x$into the equation $xy=k$and solve for $k$.

$$\begin{gathered} xy=k \\ \left(-4\right)\times 5=k \\ -20=k \end{gathered}$$

The constant of variation is $k=-20$.

Step 3. Write the equation that relates x and y.

Since the constant of variation is $k=-20$. So, the equation that relates and$y$is $xy=-20$.$x$