Lesson on Graphing Linear Inequalities

Introduction

• The lesson focuses on graphing linear inequalities.
• Builds on previous algebra skills.
• Begins by contrasting simple equations and inequalities.

Solving a Simple Equation Example

• Example: x + 5 = 8 has a solution x = 3.
• On a number line, 3 is the only solution.

Introducing Inequalities

• Example with inequality: x + 5 ≥ 8 results in x ≥ 3.
  • Solution: x can include 3 and any number larger than 3.
• Inequality solutions are sets of infinite numbers greater than a value.
• If using x + 5 > 8, x > 3 (3 not included in solutions).

Graphing Inequalities on a Coordinate Plane

• For linear equations like y = x, points on the line are solutions.
• For inequalities:
  • y ≥ x: Shade area above line.
  • y ≤ x: Shade area below line.

Solid vs. Dashed Lines

• Greater/Less than or Equal to (≥ or ≤):
  • Use solid line, points on the line included.
• Greater/Less than (> or <):
  • Use dashed line, points on the line not included.

Example 1: y ≥ 3x - 2

• Graphing steps:
  • Start at y-intercept (-2), use slope to build line.
  • Greater than or equal to; use solid line.
  • Shade above the line.
• Checking points:
  • In shaded region: Point (-5, 5) is a solution.
  • On the line: Point (2, 4) is a solution.
  • In non-shaded region: Point (6, 0) is not a solution.

Example 2: y < -12x + 4

• Graphing steps:
  • Less than sign; use a dashed line.
  • Shade below the line.
• Checking points:
  • In shaded region: Point (0, 0) is a solution.
  • On the line: Point (0, 4) is not a solution.
  • In non-shaded region: Point (6, 8) is not a solution.

Conclusion

• Points in shaded regions or on solid lines are solutions.
• Points on dashed lines or in non-shaded regions are not solutions.

Engagement

• Encourage interaction via Twitter @mashupmath.