Chapter 1.8, Problem 13E

To determine

To graph: the given inequality.

Answer to Problem 13E

  

Explanation of Solution

Given information:

  $2x-5y+19\le 0$

Calculation:

Rearrange the inequality in terms of y as follows:

  $\begin{array}{l}2x-5y+19\le 0\\ 2x+19\le 5y\\ \frac{2}{5}x+\frac{19}{5}\le y\end{array}$

Create a table by plugging the different values x in the line equation $\frac{2}{5}x+\frac{19}{5}=y$ to evaluate the value for y.

$x$	$y$
-5	1.8
-3	2.6
-1	3.4
0	3.8
1	4.2
3	5
5	5.8

Since the inequality has greater than or equal to sign $(\le )$ , solid line will be used to graph a line $\frac{2}{5}x+\frac{19}{5}=y$ .

Put the test points $\left(0,5\right)$ and $\left(0,0\right)$ in the inequality and check the true test point as follows:

Test point $\left(x,y\right)$	Inequality, $\frac{2}{5}x+\frac{19}{5}\le y$	True/False test point
$\left(0,5\right)$	$\begin{array}{c}\frac{2}{5}\left(0\right)+\frac{19}{5}\le 5\\ \frac{19}{5}\le 5\\ 3.8\le 5\end{array}$	True
$\left(0,0\right)$	$\begin{array}{c}\frac{2}{5}\left(0\right)+\frac{19}{5}\le \left(0\right)\\ \frac{19}{5}\le 0\end{array}$	False

The graph for the given inequality is shown below.