Lesson 21

In earlier lessons, students wrote and solved linear inequalities in one variable. In this lesson, they transition to linear inequalities in two variables.

Previously, students learned that the solutions to an equation in two variables are all pairs of values that make the equation true, and that, when graphed, the solutions are points on a line. Here, they learn that the solutions to inequalities in two variables also involve pairs of values. When graphed, the solutions are no longer points on a single line, but comprise a region that is bounded by a line. This region consists of all points in a plane on one side of a boundary line. That boundary line is the graph of an equation related to the inequality.

Students begin by noticing that the plots of solutions and non-solutions occupy different parts of a coordinate plane. Next, they think about the boundary line between the two regions and whether it is a part of the solution. Finally, students write some inequalities given graphs that represent solution regions.

The colored pencils are optional. If used in the first activity, each student needs 2 different colors. As an alternative to two colors, students could just write two different symbols.