Chapter 1.8, Problem 11E

To determine

To graph: the given inequality.

Answer to Problem 11E

  

Explanation of Solution

Given information:

  $2x+4y\ge 7$

Calculation:

Rearrange the inequality in terms of y as follows:

  $\begin{array}{l}2x+4y\ge 7\\ 4y\ge 7-2x\\ y\ge \frac{7}{4}-\frac{2}{4}x\end{array}$

Create a table by plugging the different values x in the line equation $y=\frac{7}{4}-\frac{2}{4}x$ to evaluate the value for y.

$x$	$y$
-5	$\frac{17}{10}$
-3	$\frac{13}{4}$
-1	$\frac{9}{4}$
0	$\frac{7}{4}$
1	$\frac{5}{4}$
3	$\frac{1}{4}$
5	$-\frac{3}{4}$

Since the inequality has greater than or equal to sign $(\ge )$ , solid line will be used to graph a line $y=\frac{7}{4}-\frac{2}{4}x$ .

Put the test points $\left(4,0\right)$ and $\left(0,0\right)$ in the inequality and check the true test point as follows:

Test point $\left(x,y\right)$	Inequality, $y\ge \frac{7}{4}-\frac{2}{4}x$	True/False test point
$\left(4,0\right)$	$\begin{array}{l}0\ge \frac{7}{4}-\frac{2}{4}\left(4\right)\\ 0\ge \frac{7}{4}-\frac{8}{4}\\ 0\ge -\frac{1}{4}\end{array}$	True
$\left(0,0\right)$	$\begin{array}{l}0\ge \frac{7}{4}-\frac{2}{4}\left(0\right)\\ 0\ge \frac{7}{4}\end{array}$	False

The graph for the given inequality is shown below.