Q18. - Algebra 1

Question

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

$y=-3$ when $x=1$

Step-by-Step Solution

Answer

The inverse variation equation is $\mathit{x}\mathit{y}\mathbf{=}\mathbf{-}\mathbf{3}$.

Step 1. Inverse variation.

$y$ varies inversely as $x$ if there is some nonzero constant $k$ such that $xy=k$, where $x,y\ne 0$.

Step 2. Substitute.

Substitute for $-3$ and 1 for $x$ into $xy=k$.

 $$\begin{gathered} 1\cdot \left(-3\right)=k \\ -3=k \end{gathered}$$

Step 3. Write the conclusion.

The constant of the variation is $-3$. Therefore, the inverse variation equation is $xy=-3$.