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.
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 ; 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 if the stated inequality is . Shade below the line if . Have students solve for 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.
General Tip. Students can misinterpret an inequality such as as an inequality in one variable and incorrectly shade that part of the axis for which .