Chapter 6.2, Problem 75S

To determine

To plot: The graph of the given inequality.

Answer to Problem 75S

The graph of the given inequality is given below.

Explanation of Solution

Given:

The given inequality function is:

  $y\le -3x+2\dots \left(1\right)$

The domain of the inequality is $\left\{x:x\in R\right\}$ .

The table for the graph of the function $y=-3x+2$ is given as:

$x$	$-2$	$7$
$y$	$8$	$-19$

The graph of the given inequality function is given by:

  

Because $y$ is less than & equal, so the shaded region must be lies below the boundary of the graph and within the domain.

Check:

Select a point in the shaded region and verify it is a solution of the inequality.

Test for the point $\left(-5,-5\right)$

  $\begin{array}{c}-5\le -3\left(-5\right)+2\\ -5\le 17\left[\text{True}\right]\end{array}$