Chapter 5.6, Problem 25E

To determine

ToGraph:The inequality $y>-2x-4$ in a coordinate plane.

Answer to Problem 25E

The graph of the given inequality is

  

Explanation of Solution

Given:

The inequality $y>-2x-4$

Concept Used:

The graph of a linear inequality in two variables shows all the solutions of the inequality in a coordinate plane.

Calculation:

Given the inequality $y>-2x-4$

Consider the corresponding equation $y=-2x-4$

Graphing the equation $y=-2x-4$

For $x=0$

  $\begin{array}{c}y=-2x-4\text{ Substitute }x=0\\ y=-2\left(0\right)-4\\ y=0-4\\ y=-4\end{array}$

For $y=0$

  $\begin{array}{c}y=-2x-4\text{ Substitute }y=0\\ 0=-2x-4\\ 0+4=-2x-4+4\text{ Add 4 to both sides}\\ 4=-2x\end{array}$

  $\begin{array}{c}\frac{4}{-2}=\frac{-2x}{-2}\text{ Divide both sides by }-2\\ x=-2\end{array}$

The points on the equation $y=-2x-4$ are

$x$	$0$	$-2$
$y$	$-4$	$0$

Since, in the given inequality $y>-2x-4$ , the symbol is $>$

So, plotting the graph of the equation $y=-2x-4$ using a dashed line. We have,

  

Testing a point on either side of the dashed line

Consider a coordinate $\left(0,0\right)$ on right side of the dashed line.

Substituting the coordinate $\left(0,0\right)$ in the given inequality on both sides, we have

  $\begin{array}{c}y>-2x-4\\ 0>-2\left(0\right)-4\text{ Substitute }\left(0,0\right)\\ 0>0-4\\ 0>-4\text{ Which is TRUE}\end{array}$

Thus, $\left(0,0\right)$ is the solution of the given inequality.

Shading the half-plane that contains $\left(0,0\right)$ . The graph of the given inequality is

  

Conclusion:

The graph of the given inequality is