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 y=mx+b if the stated inequality is y≥mx+b. Shade below the line if y≤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.
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.