Chapter 1.8, Problem 12E

To determine

To graph: the given inequality.

Answer to Problem 12E

  

Explanation of Solution

Given information:

  $-y<2x+1$

Calculation:

Rearrange the inequality in terms of y as follows:

  $\begin{array}{l}-y<2x+1\\ y>-2x-1\end{array}$

Create a table by plugging the different values x in the line equation $y=-2x-1$ to evaluate the value for y.

$x$	$y$
-5	9
-3	5
-1	1
0	-1
1	-3
3	-7
5	-11

Since the inequality has greater than sign $(>)$ , dotted line will be used to graph a line $y=-2x-1$ .

Put the test points $\left(-1,0\right)$ and $\left(0,0\right)$ in the inequality and check the true test point as follows:

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

The graph for the given inequality is shown below.