Chapter 16.9, Problem 7MRE

To determine

To graph: the given function.

Explanation of Solution

Given information:

Given function is

  $\mathrm{y}=\frac{2}{3}\mathrm{x}-4$

Calculation:

Consider the given function,

  $\mathrm{y}=\frac{2}{3}\mathrm{x}-4$ ……. (1)

Obtain some points on the function.

Substitute 0 for x in equation (1).

  $\begin{array}{c}\mathrm{y}=\frac{2}{3}\left(0\right)-4\\ =-4\end{array}$

The point $\left(0,-4\right)$ is on the graph.

Substitute 3 for x in equation (1).

  $\begin{array}{c}\mathrm{y}=\frac{2}{3}\left(3\right)-4\\ =-2\end{array}$

The point $\left(3,-2\right)$ is on the graph.

Substitute 6 for x in equation (1).

  $\begin{array}{c}\mathrm{y}=\frac{2}{3}\left(6\right)-4\\ =0\end{array}$

The point $\left(6,0\right)$ is on the graph.

Substitute 9 for x in equation (1).

  $\begin{array}{c}\mathrm{y}=\frac{2}{3}\left(9\right)-4\\ =2\end{array}$

The point $\left(9,2\right)$ is on the graph.

Now, plot the points on rectangular coordinate axes and sketch the graph of the function as shown: