Section 3.4
Linear Inequalities In Two
Variables
Overview
• In this section we learn to graph linear
inequalities.
• It is important to recognize the finished product
of our efforts:
Continued
•
The graph of a linear inequality in two
variables will consist of:
1. A boundary line, either solid or dotted.
2. Shading on either side of the line.
Definition
• A linear inequality on two variables will be in the
form:
Ax  By
Ax  By
Ax  By
Ax  By
C
C
C
C
y  mx  b
y  mx  b
y  mx  b
y  mx  b
How to graph
1. Graph the boundary line. Use a solid
boundary line for > or <, use a dotted boundary
line for > or <.
2. Test a point—usually (0,0)—by substituting the
point into the original inequality.
3. Shade the “point side” if the point makes a true
statement. Shade opposite the “point side” if
the point makes a false statement.
Examples
x + y < -3
4x – 5y > 20
x – 5y < 0
Compound Inequalities
• “and” still means intersection, or overlap.
• “or” still means union, or everything
• Graph both inequalities using the steps
previously discussed.
• In MyLabsPlus, use the “paint can” to
identify and shade your solution region.
• On paper, shade your solution region
darker than the rest of the graph.
Examples
x – y > 2 and x > 3
x + y < 2 or y > 3