Graphing Inequalities

In this section, we learn about graphing linear inequalities in two variables. These are of the form: ax + by < c (a, b, and c are real numbers, a and b are not both zero, and < can be >, ≥, or ≤). There are two main methods to graph a linear inequality in two variables. In the first scenario, we can replace the inequality symbol with an equality symbol. We graph the resulting line, which is known as the boundary line. This boundary line separates the solution region from the non-solution region. We use a test point to see which area of the graph (side of the boundary line) to shade as the solution region. Alternatively, we can solve the inequality for y, graph the boundary line, and shade the solution region based on the given inequality symbol. If we have a less than or less than or equal to, we shade below the boundary line. If we have a greater than or greater than or equal to, we shade above the boundary line.