Q5. - Algebra 1

Question

Graph an inverse variation equation in which $y=16$ when $x=4$.

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 16 for $y$, 4 for $x$ into the equation $xy=k$ and solve for $k$.

$$\begin{gathered} xy=k \\ 4\times 16=k \\ 64=k \end{gathered}$$

The constant of variation is $k=64$. So, the equation that relates $x$ and $y$ is $xy=64$.

Step 3. Plot the points on the graph.

Create the table of values satisfying $y=\frac{64}{x}$. Choose values for $x$ and $y$ that have a product of 64.

$x_1$	$y_1$
2	32
4	16
$-2$	$-32$
$-4$	$-16$
8	8
$-8$	$-8$
10	64
$-10$	$-6.4$

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

The graph obtained is: