Chapter 6.5, Problem 16PPS

To determine

Graph the inequality $x-y\le 3$ .

Explanation of Solution

Given:

The inequality is $x-y\le 3$ .

Calculation:

Simplify the inequality as follows:

  $\begin{array}{l}x-y\le 3\\ x-x-y\le -x+3\\ -y\left(-1\right)\le -x\left(-1\right)+3\left(-1\right)\\ y\ge x-3\mathrm{......}\left(1\right)\end{array}$

Thus, the graph of $x-y=3$ ,

Consider x = 0,

  $\begin{array}{l}0-y=3\\ y=-3\end{array}$

Thus, the coordinate is (0, -3).

Consider y = 0,

  $\begin{array}{c}x-0=3\\ x=3\end{array}$

Thus, the coordinate is (3, 0).

The graph of the line is shown below:

  

Apply the inequality in the graph on the upward of the graph as inequality is greater than equal to in equation (1).