Chapter 8.9, Problem 21E

To determine

To graph:

The given linear inequality.

Answer to Problem 21E

The graph of our given inequality would look like:

  

Explanation of Solution

Given:

An inequality:

  $y>-3x$

Calculation:

First of all, we will replace the inequality sign with an equal to sign to graph the boundary line as: $y=-3x$ . Since we have a greater than sign $(>)$ , so our boundary line will be a dashed line as shown below:

  

Now, we will test a point $(1,0)$ to shade in the correct region.

  $\begin{array}{l}y>-3x(\text{Given inequality)}\\ 0>-3(1)(\text{Substituting }x=1\text{ and }y=0)\\ 0>-3\end{array}$

Since point $(1,0)$ satisfies our given inequality, so we will shade in the region, which includes point $(1,0)$ .

Upon shading in the region that includes point $(1,0)$ , we will get our required graph as shown below: