Study Guide: Section 7-8

Graphing Inequalities in Two Variables

Practice Problems

Directions: Graph each inequality on a coordinate plane. Determine whether the boundary line is solid or dashed, and shade the appropriate half-plane.

1. y < 4

Boundary line: y = 4 (dashed horizontal line).
Region: Open half-plane shaded below the line.

Solution Graph: Solution Graph for Problem 1

2. 3x < y (or y > 3x)

Boundary line: y = 3x (dashed line through origin, slope 3).
Region: Open half-plane shaded above the line.

Solution Graph: Solution Graph for Problem 2

3. 2x − 3y ≤ 6

Boundary line: 2x − 3y = 6 (solid line, intercepts at (3, 0) and (0, −2)).
Region: Closed half-plane shaded above and on the line.

Solution Graph: Solution Graph for Problem 3

4. −5x + 2 ≥ y (or y ≤ −5x + 2)

Boundary line: y = −5x + 2 (solid line, y-intercept (0, 2), slope −5).
Region: Closed half-plane shaded below and on the line.

Solution Graph: Solution Graph for Problem 4

5. x − y ≥ 1 (or y ≤ x − 1)

Boundary line: x − y = 1 (solid line, intercepts at (1, 0) and (0, −1)).
Region: Closed half-plane shaded below and on the line.

Solution Graph: Solution Graph for Problem 5

6. −x > y (or y < −x)

Boundary line: y = −x (dashed line through origin, slope −1).
Region: Open half-plane shaded below the line.

Solution Graph: Solution Graph for Problem 6