Linear Equations, Inequalities and Systems

Lesson 7

Objective

Write linear inequalities from graphs.

Common Core Standards

Core Standards

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  • A.CED.A.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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

  • A.REI.D.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.

Foundational Standards

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  • 7.EE.B.4.B

  • 8.EE.B.5

  • 8.EE.B.6

Criteria for Success

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  1. Identify features of linear inequalities from graphs and represent them algebraically. 
  2. Test points in a linear inequality and verify graphically. 
  3. Include domain and range restrictions in graphing and writing linear inequalities. 

Anchor Problems

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Problem 1

Write the inequality that is graphed below. 

Guiding Questions

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Problem 2

Below are several marked points. Write an inequality that does not have the Xs as solutions but has the closed dots as solutions. 

Guiding Questions

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Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

Target Task

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Write an inequality for the following graph and name two points that are solutions and two points that are not solutions. Verify the solutions graphically.