For a complete lesson on graphing linear inequalities, go to http://www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to graph inequalities in two variables. For example, to graph y is less than x + 2, the first step is to graph the boundary line y = x + 2, using the chart method from lesson 4B. Note that greater than or less than means that the boundary line will be dotted, and greater than or equal to or less than or equal to means that the boundary line will be solid. To determine which side of the boundary line to shade, substitute a test point, such as (0, 0), into the original inequality, y is less than x + 2. Since (0) is less than (0) + 2, or 0 is less than 2, is a true statement, the side of the line that contains the point (0, 0) is shaded.