91Ó°ÊÓ

The given boundary line is $x+2y=-2.$We have to write the inequality shown by the shaded region in the graph with the boundary line.

The line $x+2y=-2$is the boundary line. On one side of the line are the points with $x+2y>-2$and on the other side of the line are the points with $x+2y<-2.$

Let’s test the point $\left(0,0\right),$and see which inequality describes its side of the boundary line.

At $(0,0),$which inequality is true:

$$\begin{gathered} x+2y>-2orx+2y<-2 \\ 0+2\left(0\right)>-2or0+2\left(0\right)<-2 \\ 0>-2\left[True\right]or0<-2\left[False\right] \end{gathered}$$

Since, $x+2y>-2$is true, the side of the line with $\left(0,0\right),$is the solution. The shaded region shows the solution to the inequality $x+2y>-2.$

Since the boundary line is graphed with a solid line, the inequality includes the equal sign.

The graph shows the inequality $x+2yâ‰\yen -2.$