Section 3.2: Graphing Inequalities
Graphing inequalities involves shading regions on a number line or coordinate plane to represent solutions.
- Use an open circle for < or >, closed circle for ≤ or ≥ on a number line.
- For two-variable inequalities, shade the side of the line that satisfies the inequality.
- Test a point not on the line (usually (0,0)) to determine which region to shade.
Example 1: Number Line
Graph \( x > 3 \) on a number line.
Use an open circle at 3 and shade to the right: all numbers greater than 3.
Example 2: Coordinate Plane
Graph \( y \le 2x + 1 \).
Step 1: Graph the line \( y = 2x + 1 \) (solid line because ≤).
Step 2: Test point (0,0): \( 0 \le 2*0 + 1 \) → \( 0 \le 1 \) True → shade below the line.
Practice Problems
- Graph \( x \le -2 \) on a number line
- Graph \( y > -x + 3 \) on a coordinate plane
- Graph \( x > -1 \) and \( x \le 4 \) (compound inequality)
- Graph \( y \ge \frac{1}{2}x - 1 \)
- Test a point to decide shading for \( y < -2x + 4 \)