In this lesson, students begin looking at solutions to inequalities in two variables. They make use of their understanding that solutions to linear equations in two variables can be represented on a graph with a line. 

Students 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. The boundary line is the graph of an equation related to the inequality. The solution region includes all points in a plane on one side of the boundary. The region also includes the boundary line itself when the inequality is not strict and allows for the two sides of the expression to be equal. 

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.