# 6.7: Linear Inequalities in Two Variables

Difficulty Level:

**At Grade**Created by: CK-12## 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*}y 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*}

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

Date Created:

Feb 22, 2012
Last Modified:

Aug 22, 2014
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