Lesson 6: 5-6 Graphing Inequalities in Two Variables

If an inequality involves < or >, is the boundary line included in the solution?

If an inequality involves = or =, is the boundary line included in the solution?

boundary
half-plane
closed half-plane
open half-plane

A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

SAT questions related to inequalities: 5-4-13,7-4-5,4-4-19,8-3-6,1-4-28,5-3-7,6-3-14;

The solution set of a linear inequality is the set of all ordered pairs that makes the statement true. The solution set of an inequality in two variables graphed on a coordinate plane is not linear. Instead, it has a linear boundary and it covers a region called a half-plane.

Ranjan writes and edits short articles for a local newspaper. It takes him about an hour to write an article and about a half-hour to edit an article. If Ranjan works up to 8 hours a day, how many articles can he write and edit in one day?

Students may need a quick refresher on slope-intercept form before they graph inequalities. Remind students that slope-intercept form is y = mx + b.

If some students have trouble working with the numbers in Example 4, then as an alternative problem, have them write and solve an inequality for the budget situation in the Why? section at the beginning of the lesson. The inequality they should write, solve, and then graph is 8x + 12y = 70.

Extension: Challenge students to write an inequality for the graph whose boundary passes through the points at (4, -2) and (-3, -2) and whose solution set contains the boundary and all the points above the boundary.

Practice: Exercises 1 - 9

Exercises 42 - 47

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