Answer
Please see the graph.
Work Step by Step
Red line: $2x\lt3y+8$
Blue line: $y\ge-2$
Let's use the point $(0,0)$ to determine what sides of the lines to shade.
Red line: $2x\lt3y+8$
$2x\lt3y+8$
$2*0 \lt 3*0+8$
$0 \lt 0+8$
$0 \lt 8$ (true)
We'll shade the side of the red line that does have $(0,0)$ on that side. We have a "less than" sign, so we'll use a dotted line.
Blue line: $y\ge-2$
$y \ge -2$
$0 \ge -2$ (true)
We'll shade the side of the blue line that doesn't have $(0,0)$ on that side. We have a "greater than or equal to" sign, so we'll use a solid line.
The intersection of the two areas is the area that is shaded blue and red.
