Q3. - Algebra 1

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 $\mathit{x}\mathbf{=}\mathbf{12}$.

Step-by-Step Solution

Answer

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

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 $x$ and $y$ is $xy=-24$.