Chapter 8, Problem 25CT

To determine

To graph:

The given linear inequality.

Answer to Problem 25CT

The graph of our given inequality would look like:

  

Explanation of Solution

Given:

An inequality:

  $y\le 3x-5$

Calculation:

First of all, we will replace the inequality sign with an equal to sign to graph the boundary line as: $x+2y=6$ . Since we have a less than or equal to sign $(<)$ , 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.

  $\begin{array}{l}y\le 3x-5(\text{Given inequality)}\\ 0\le 3(0)-5(\text{Substituting }x=0\text{ and }y=0)\\ 0\le 0-5\\ 0\le -5\end{array}$

Since point $(0,0)$ doesn’t satisfy our given inequality, so we will shade in the region, which excludes point $(0,0)$ .

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