Graphing Linear Inequalities

Objective: Graphing Linear Inequalities on the Coordinate Plane

October 23, 2024

Page 1

Do Now: Thinking Task

Given the following inequality, complete the tasks below:

1. Re-write the inequality in slope-intercept form.
2. Identify the slope and y-intercept.
3. Determine if the point (-3,-2) is a solution to this inequality. Justify your response.

Key Terms

• Slope-Intercept Form: The equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.

Page 2

Graphing Linear Inequalities on a Coordinate Plane

1. Solve the inequality for y and rewrite in slope-intercept form.

   • Remember to reverse the inequality symbol if you multiply or divide by a negative!

2. Graph the line as normal, but note:

   • Use a dashed line for \geq and \leq
   • Use a solid line for > and <

3. Since inequalities represent a range of solutions, we need to identify where the points are possible solutions:

   • Shade above the line for >
   • Shade below the line for <

4. Check your graph by using a test point (commonly (0,0) if it lies within the graph).

Important Notes:

• Shading indicates where the solutions to the inequality lie.

Page 3

Practice Graphing: Example Problems

Exercise 1:
Graph the inequality y \leq -1x - 3

Exercise 2:
Graph the inequality y > -2 - 3x

Page 4

More Practice Graphing

Exercise 3:
Graph the inequality 2x - 5y \leq -20

• Rearranging gives y \geq \frac{2}{5}x + 4

Exercise 4:
Graph the inequality x > -2

Exercise 5:
Graph the inequality 2x - y \leq -1

• Rearranging gives y \geq 2x + 1

Page 5

Match It Up!

Match each inequality with the correct corresponding graph:

1. 2x - y > 6
2. y \leq 2x - 6
3. 2x < y + 6
4. 2x - 6 \leq y