Chapter 6.5, Problem 19PPE

To determine

To Graph: The given inequality.

Explanation of Solution

Given information:

The given inequality is $y\le \frac{1}{2}x-3$

Consider the line $y=\frac{1}{2}x-3$

  $\begin{array}{l}y=0\Rightarrow \\ 0=5x-5\\ x=6\\ x=0\Rightarrow \\ y=-3\end{array}$

Draw the solid line passing through $(0,-3)\&(6,0)$ and then shade below the region.

Graph:

The graph of $y\le \frac{1}{2}x-3$ is shown below.

  

Hence, the shaded region is the solution of the given inequality.