# 6.7: Linear Inequalities in Two Variables

Difficulty Level:

**At Grade**Created by: CK-12Turn In

## Learning Objectives

At the end of this lesson, students will be able to:

- Graph linear inequalities in one variable on the coordinate plane.
- Graph linear inequalities in two variables.
- Solve real-world problems using linear inequalities.

## Vocabulary

Terms introduced in this lesson:

- dashed line/solid line

## Teaching Strategies and Tips

In this lesson, students learn to graph linear inequalities on the coordinate plane.

- Students draw dashed lines for the strict inequalities \begin{align*}(<, >)\end{align*}
(<,>) ; interpret this as excluding the points on the line from the solution set. Students draw solid lines for the inequalities \begin{align*}\le, \ge\end{align*}≤,≥ ; interpret this as including the points on the line in the solution set. - Have students shade those regions of the plane which satisfy the given inequalities.
- As a general rule, shade above the line \begin{align*}y = mx + b\end{align*}
y=mx+b if the stated inequality is \begin{align*}y \ge mx + b\end{align*}y≥mx+b . Shade below the line if \begin{align*}y \le mx + b\end{align*}y≤mx+b . Have students solve for \begin{align*}y\end{align*} first. See Examples 5-7. - Graphing inequalities on the coordinate plane is a step up from graphing on the number line and requires more care.

Use Examples 1 and 2 to motivate graphing the *absolute value* inequalities in Examples 3 and 4.

- Have students rewrite the absolute value inequality as a compound inequality first.

In Examples 8 and 9 and Problems 13 and 14 in the *Review Questions*,

- Point out that quadrant I is the only quadrant used because the variables should be positive.
- Only the points with integer coordinates are possible solutions in Example 9.

## Error Troubleshooting

General Tip. Students can misinterpret an inequality such as \begin{align*}x > 2\end{align*} as an inequality in one variable and incorrectly shade that part of the \begin{align*}x-\end{align*}axis for which \begin{align*}x > 2\end{align*}.

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Tags:

Absolute Value
absolute value inequalities
Activities
(36 more)
Answer Key
Answers
Assessment
CK.MAT.ENG.TE.1.Algebra-I.6
Common Misconceptions
compound inequalities
Concept Check and Troubleshooting
Differentiated Instruction
discrete solutions
Enrichment
inequalities
inequality
inequality notation
infinite solutions
Inquiry Process
interval of values
linear inequalities in one variable
linear inequalities in two variables
multi-step inequality
Pacing
Problem Sets
Problem Solving
Quizzes
Science Inquiry
set notation
solution graph
Solution Key
solution set
Solutions
Teacher Edition
Teaching Strategies
Teaching Strategies and Tips
Testing
Tests
two-step inequality
Worksheets

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Date Created:

Feb 22, 2012
Last Modified:

Aug 22, 2014
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