# Lesson 21

From One- to Two-Variable Inequalities

These materials, when encountered before Algebra 1, Unit 2, Lesson 21 support success in that lesson.

### Lesson Narrative

In this lesson, students begin the move from one-variable inequalities to two-variable inequalities. They plot points on a coordinate plane that fit a one-variable inequality to see how that divides the plane. Then, students select points that are on, above, or below a line that represents a given equation. In the associated Algebra 1 lesson, students draw the graph that represents solutions to two-variable inequalities. The work of this lesson supports that learning by providing some additional work that builds on their current understanding of one-variable inequalities and linear equations.

Students look for regularity in repeated reasoning (MP8) when they use the points selected by the class that satisfy a one-variable inequality to determine the region of the plane that represents the solution in two dimensions.

### Learning Goals

Teacher Facing

• Draw the solutions to one-variable inequalities on a coordinate plane.
• Write points that are on, above, or below a line represented by a given equation.

### Student Facing

• Let’s look at inequalities in two dimensions.