Chapter  6.7 Graphs of Linear Inequalities

Pindling College Algebra   by Example  Series

Key Concepts: Graphs of inequalities and systems of inequalities.

Skills to Learn.

1. Know how to graph inequalities and determine the location of the half-plane

2. Know how to graph systems of inequalities and locate the half-planes

Convention: Red boundaries are not included and Blue boundaries are included in the graph.

Example 1 Graph Graph does not include the line Locate half plane: Test if include the origin (0, 0) Test: Not True so half plane on other side of line (away from the origin)

Graph:

Example 2 Graph Graph includes the line Locate half plane: Test if include the origin (0, 0) Test: Not True so half plane on other side of line (away from the origin)

Graph:

Example 3 Graph Graph does not includes the line Locate half plane: Test if include the origin (0, 0) Test: Is True so the origin is a part of half plane

Graph:

Example 4 Graph Graph does not includes the line Locate half plane: Test origin (0, 0) In conclusive Try (8, 1) Test: Not True so on other side of half-plane not including (8, 1) Try (6, 3) Test: Is True so the (6, 3) is a part of half plane

Graph:

Systems of Inequalities

Example 5 Graph (1) (2) (3) (4) These are vertical lines (x = a) and horizontal lines (y = b) Half plane: Test not needed here

Graph:

Example 6 Graph (1) (2) (3) Test - Half plane Equation (1): Origin (0, 0) True, so origin a part of half plane Equation (2): Origin (0, 0) True, so origin a part of half plane Equation (3): Origin (1, 1) 1 > 0 is True, so half plane on right of x = 0

Graph:

Example 7 Graph (1) (2) (3) Test - Half plane Equation (1): Origin (0, -1) True, so (0, -1) is a part of half plane Equation (2): Origin (0, 0) True, so origin a part of half plane Equation (3): Origin (0, 0) 0 < 3 0 is True, so half plane below y = 3

Graph:

Example 8 Graph (1)    rewrite as     (2)    rewrite as     (3) Test - Half plane Equation (1): Origin (0, -1) True, so (0, -1) is a part of half plane Equation (2): Origin (0, 0) True, so origin a part of half plane Equation (3): Origin (0, 0) 0 < 3 0 is True, so half plane below y = 3

Graph: