Q7. - Algebra 1

Question

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

$y=3$ when $x=-10$

Step-by-Step Solution

Answer

The graph obtained is:

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. Write the equation that relates x and y .

Since $y$ varies inversely as $x$ an inverse variation equation is given by $xy=k$ so, substitute 3 for $y, -10$ for $x$ into the equation $xy=k$, and solve for $k$.

$$\begin{gathered} xy=k \\ \left(-10\right)\times 3=k \\ -30=k \end{gathered}$$

The constant of variation is $k=-30$. So, the equation that relates $x$ and $y$ is $xy=-30$.

Step 3. Plot the points on the graph.

Create the table of values satisfying $y=-\frac{30}{x}$. Choose values for $x$ and $y$ that have a product of $-30$.

$x_1$	$y_1$
$-2$	15
$-5$	6
2	$-15$
5	$-6$
6	$-5$

Plot each point and draw a smooth curve that connects these points. 

The graph obtained is: