Lesson 19: Graphing Linear Inequalities
A linear inequality is like a linear equation but instead of an equals sign, it uses:
- < (less than)
- > (greater than)
- ≤ (less than or equal to)
- ≥ (greater than or equal to)
Example: y > 2x + 1 means all points above the line y = 2x + 1.
Steps to Graph a Linear Inequality
- Graph the corresponding line y = mx + b.
- Use a solid line for ≤ or ≥, and a dashed line for < or >.
- Pick a test point (0,0) unless it is on the line.
- Plug the test point into the inequality:
- If true → shade the side of the line with the test point.
- If false → shade the opposite side.
Example: Graph y ≤ x + 2
- Graph the line y = x + 2 (solid line because ≤)
- Pick test point (0,0): 0 ≤ 0 + 2 → True
- Shade the side of the line that includes (0,0)
Practice Problems
- Graph y > 2x - 1
- Graph y ≤ -x + 3
- Graph 2x + y < 4
- Graph y ≥ 1/2 x - 2
Lesson Summary
- Linear inequalities are like linear equations with <, >, ≤, or ≥.
- Use solid lines for ≤ and ≥, dashed lines for < and >.
- Shade the side that satisfies the inequality using a test point.