How Do You Graph Inequalities?

The first step in graphing an inequality is to draw the line that would be obtained, if the inequality is an equation with an equals sign. The next step is to shade half of the graph.

To draw the line determined by the inequality, write the inequality with an equals sign. Then find two points on the line. An easy way to do this is to locate the x- and y-intercepts, if they exist. To find the x-intercept, set y = 0, solve the equation for x and plot the resulting point on the x-axis. If no x-intercept exists because the equation describes a horizontal line, find the y-intercept by setting x = 0. Then locate another point on the line, such as x = 2.

Once two points are located, draw a line through them. If the inequality uses the sign for “less than or equal to” or “greater than or equal to,” the line should be solid. If the inequality uses the sign for “less than” or “greater than,” the line should be dotted to indicate that points on the line are not included in the range of points specified by the inequality.

Finally, determine which part of the graph to shade. This is done by testing a point that is not on the line. For example, if the origin of the graph is not on the line, set x = 0 and y = 0 and see if the resulting inequality is true. If it is, the part of the graph that contains that point should be shaded. If the resulting inequality is false, the part of the graph on the other side of the line should be shaded.