Question

Assume that $\mathit{y}$varies inversely as $\mathit{x}$. Write an inverse variation equation that relates $\mathit{x}$and $\mathit{y}$.

role="math" localid="1648013702502" $\mathit{y}\mathbf{=}\mathbf{5}$when$\mathit{x}\mathbf{=}\mathbf{10}$.

Short answer

An inverse variation equation that relates$x$ and$y$ is $\mathit{x}\mathit{y}\mathbf{=}\mathbf{50}$.

Step-by-step solution

Step 1. Define the meaning of variation.

The changing of variable parameters is called a variation.

Step 2. Define an inverse variation equation.

The inverse variation equation of two variables$x$ and$y$ is given by

$xy=k$

Where,role="math" localid="1648013829424" $k$is called the constant of variation.

Step 3. Write an variation equation that relates x and y for y=5 when x=10.

Assume that$y$ varies inversely as $x$.

The inverse variation equation is given by

$xy=k$

Substitute$x=10$ and $y=5$.

$\begin{array}{l}10\times 5=k\\ 50=k\\ k=50\end{array}$

Substitute $k=50$in $xy=k$.

$xy=50$

Therefore an inverse variation equation that relates role="math" localid="1648014076213" $x$and $y$is $xy=50$.