Question

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

$\mathit{y}\mathbf{=}\mathbf{-}\mathbf{2}$when $\mathit{x}\mathbf{=}\mathbf{12}$.

Short answer

An inverse variation equation that relates $x$and $y$is$\mathit{x}\mathit{y}\mathbf{=}\mathbf{-}\mathbf{24}$.

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,$k$ is called the constant of variation.

Step 3. Write an variation equation that relates x and y for y=−2 when x=12.

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

The inverse variation equation is given by

$xy=k$

Substitute$x=12$ and $y=-2$.

$\begin{array}{l}12(-2)=k\\ -24=k\\ k=-24\end{array}$

Substitute$k=-24$ in $xy=k$.

$xy=-24$

Therefore an inverse variation equation that relates role="math" localid="1648014671581" $x$and $y$is $xy=-24$.