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# 6.7: Linear Inequalities in Two Variables

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 $(<, >)$; interpret this as excluding the points on the line from the solution set. Students draw solid lines for the inequalities $\le, \ge$; 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 $y = mx + b$ if the stated inequality is $y \ge mx + b$. Shade below the line if $y \le mx + b$. Have students solve for $y$ 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 $x > 2$ as an inequality in one variable and incorrectly shade that part of the $x-$axis for which $x > 2$.

Feb 22, 2012

Aug 22, 2014