Write a list of four to eight linear inequalities in one column and their corresponding graphs in a separate column in random order. Have students identify which graph corresponds to which equation based on the slope and y-intercept of the line, the shading and the type of boundary line (solid or dotted). For an additional challenge, write some of the equations in a form other than slope-intercept form (for example, 2x < y + 1).
Write a graph of a linear inequality, its corresponding equation and a list of roughly a dozen (x, y) coordinate pairs on the board or handout. Ask individual students to come to the board or say for the class whether each point is a solution to the linear inequality and how they know this. Make sure the students understand that you can verify the solution either by plugging the coordinates into the equation or by placing the coordinate point on the graph. For example, verify that (0,1) is a solution to y < x + 2 by substituting 0 for x and 1 for y to get the true inequality 1 < 0 + 2. Verify that it is a solution by labeling the point on the graph and seeing that it is within the shaded region below the dotted line y = x + 2.
Give students a list of problems with linear inequalities and two or three coordinate points. For each problem, make at least one of the coordinate points fall directly on the line. Students will have to use their knowledge of the difference between a solid line for ≥ and ≤ inequalities and a dotted line for < and > inequalities. For the former, points on the line are solutions to the inequality, while for the latter they are not.
Introduce students to compound inequalities, which are groups of inequalities joined by AND or OR. The solution to compound inequalities joined by AND is the intersection or overlap of the shaded areas. The solution to compound inequalities joined by OR is the union or combined region of the two areas. Give students a set of AND and OR compound inequalities and have them show whether given points are solutions to the inequalities.