The first thing you have to do is to figure out what the equation for the line is then worry about the greater than/less than part. The dotted line goes through the y axis at -2, so the "b" part of our line is -2. From the -2 we can go up 3 and the to right 2 to land on the next point of our line that crosses through the grids of the graph. So that means that the slope is 3/2. So the equation for that line is y = 3/2x - 2. NOW we worry about the inequality part of it. The shading indicates that the points that fall within it are part of the solution. Since the line is dotted, the solution we pick will not contain an "or equal to". To see which side of the line we need to choose, let's pick a point and see if that point subbed in for x and y make the inequality true or not. Let's try (0, 0). If we sub in 0 for x and 0 for y into our first inequality statement (one of the 2 that doesn't have an "or equal to" in it) it looks like this: [tex]0\ \textless \ \frac{3}{2} (0)-2[/tex] which says, after solving, that 0 is less than -2. 0 is not less than -2, so that is not our correct choice. The last one, using the greater than sign, looks like this: [tex]0\ \textgreater \ \frac{3}{2}(0)-2 [/tex] and this says that 0 is greater than -2. 0 IS greater than -2, so D is our choice.
