One linear inequality in two variables divides the plane into two half-planes. To graph the inequality, graph the equation of the boundary. Use a solid line if the symbol ≤ or ≥ is used because the boundary is included in the solution. Use a dashed line if < or > is used to indicate that the boundary is not part of the solution. Shade the appropriate region. Unless you are graphing a vertical line the sign of the inequality will let you know which half-plane to shade. If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line. For a vertical line, larger solutions are to the right and smaller solutions are to the left. A system of two or more linear inequalities can divide the plane into more complex shapes.
Graph y < 2x + 1
Graph the system of linear inequalities.
Graphing the three lines and shading the region enclosed, we get the figure below.