Q2. - Algebra 1

Question

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

Step-by-Step Solution

Answer

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

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 $xy=-20$.$x$