Question

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

$y=8$when$x=6$

Short answer

The graph obtained is:

Step-by-step solution

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 $x$and inverse variation equation is given by $xy=k$so, substitute 8 for $y$, 6 for $x$into the equation $xy=k$, and solve for $k$.

$$\begin{gathered} xy=k \\ 6\times 8=k \\ 48=k \end{gathered}$$

The constant of variation is $k=48$. So, the equation that relates $x$ and$y$is $xy=48$.

Step 3. Plot the points on the graph.

Create the table of values satisfying $y=\frac{48}{x}$. Choose values for $x$and $y$that have a product of 48.

$x_1$	$y_1$
$-8$	$-6$
$-6$	$-8$
$-2$	$-24$
0	Undefined
2	24
6	8
8	6
12	4

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

The graph obtained is: