Graphing Linear Inequalities on a Grid MATH 017 Intermediate Algebra S. Rook

2 Overview Section 3.6 (Objective 1) in the textbook –Graphing Linear Inequalities including finding test points and shading

3 Graphing Linear Inequalities We know 3 ways to graph: –Table of Values –Intercepts –By slope and y-intercept No different than graphing linear equalities except for: –Whether the line is solid (≤, ≥) or broken ( ) –Shading one side of the line

4 Test Points and Shading After constructing the line, pick a test point that does NOT lie on the line –(0, 0) is often a good choice Substitute the x and y values into the inequality and simplify –If the statement is true, shade the side WITH the test point –If the statement is false, shade the side WITHOUT the test point

5 Graphing Linear Inequalities on a Grid (Example) Ex 1: Graph y ≥ -3x – 1

6 Graphing Linear Inequalities on a Grid (Example) Ex 2: Graph 5x – 3y < 12

7 Graphing Linear Inequalities on a Grid (Example) Ex 3: Graph x ≤ 2y

8 Graphing Linear Inequalities on a Grid (Example) Ex 4: Graph

9 Summary After studying these slides, you should know how to do the following: –Graph a linear inequality on a coordinate grid and correctly shade one side of the line based on a test point