Chapter 2.2, Problem 25E

To determine

To graph: the given inequality.

Answer to Problem 25E

  

Explanation of Solution

Given information:

  $y\le -\frac{1}{3}x+2$

Calculation:

Make a table for the line $y=-\frac{1}{3}x+2$ by substituting the value of x and evaluating y as shown below.

$x$	0	1	2	3	$-1$	$-2$	$-3$
$y$	2	$\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$	$\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$	1	$\raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$	$-\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$	3

Since the inequality has less than or equal to sign $(\le )$ , a solid line will be used to graph these points.

  

Now, substitute the test points in the given inequality and find the true test point as follows:

Test Points	$y\le -\frac{1}{3}x+2$	True or false
$\left(0,0\right)$	$\begin{array}{l}0\le -\frac{1}{3}\left(0\right)+2\\ 0\le 2\end{array}$	True
$\left(3,3\right)$	$\begin{array}{l}3\le -\frac{1}{3}\left(3\right)+2\\ 3\le -1+2\\ 3\le 1\end{array}$	False

Shade the region of graph having true test point as shown below.