Shading half of the plane to show the solution set.
Boundary Line
To graph the inequality, we have to draw the boundary line. The equation of a boundary line is written by replacing the inequality symbol from the inequality with an equals sign.
Inequality
Boundary Line
y< -4
y=-4
Notice that the equation for this boundary line only has one variable. This equation is telling us that each and every point that lies on the line will have a y-coordinate equal to -4. This means that it is a horizontal line. Also, the inequality is strict, so the points on the boundary line are not included in the solution set. We show this by drawing a dashed line.
Shading the Plane
The inequality y<-4 describes all values of y that are less than - 4. This means that every possible (x,y) coordinate pair with a y-value that is less than -4 needs to be included in the shading. In other words, we will shade the region below the boundary line.
