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≥ 1
y=1
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 -1. This means that it is a horizontal line. Also notice that the inequality is notstrict, so the points on the boundary line are included in the solution set. We have shown this by drawing a solid line.
Shading the Plane
The inequality y≥-1 describes all values of y that are greater than or equal to -1. This means that every possible (x,y) coordinate pair with a y-value that is greater than or equal to -1 needs to be included in the shading. In other words, since the sign of the inequality is ≥, we will shade the region above the boundary line.
