Chapter 8, Problem 27CR

To determine

To graph:

The given linear inequality.

Answer to Problem 27CR

The graph of our given inequality would look like:

  

Explanation of Solution

Given:

An inequality:

  $y\le 2x+3$

Calculation:

First of all, we will replace the inequality sign with an equal to sign to graph the boundary line as: $y=2x+3$ . Since we have a less than or equal to sign $(\le )$ , so our boundary line will be a solid line as shown below:

  

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

  $\begin{array}{l}y\le 2x+3(\text{Given inequality)}\\ 0\le 2(0)+3(\text{Substituting }x=0\text{and }y=0)\\ 0\le 3\end{array}$

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

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