Graphing Linear Inequalities
in Two Variables
Linear Inequalities
• A linear inequality in two variables can be
written in any one of these forms:




Ax + By < C
Ax + By > C
Ax + By ≤ C
Ax + By ≥ C
• An ordered pair (x, y) is a solution of the linear
inequality if the inequality is TRUE when x and y
are substituted into the inequality.
Example 1
•
Which ordered pair is a solution of
5x - 2y ≤ 6?
A.
B.
C.
D.
(0, -3)
(5, 5)
(1, -2)
(3, 3)
Graphing Linear Inequalities
• The boundary line will be a:
– Solid line when ≤ and ≥ are used.
– Dashed line when < and > are used.
• Graph will be shaded on one side of the
boundary line to show the solutions.
Graphing Linear Inequalities
STEPS:
1. Graph the boundary line:
 ≤ and ≥ will use a solid curve.
 < and > will use a dashed curve.
2. Test a point NOT on the boundary line to
determine which side of the line
includes the solutions.
 If your test point is a solution, shade that
side.
 If your test points is NOT a solution, shade
the opposite side.
Example 2
• Graph the inequality x ≤ 4 in a coordinate
plane.
• HINT:
– Decide whether to use
a solid or dashed line.
y
5
• Use (0, 0) as a
test point.
• Shade where the
solutions will be.
x
-5
-5
5
Example 3
• Graph 3x - 4y > 12 in a coordinate plane.
• Sketch the boundary line of the graph.
– Find the x- and y-intercepts and
plot them.
5
– Solid or dashed line?
y
• Use (0, 0) as a
test point.
• Shade where the
solutions are.
x
-5
-5
5
Example 4:
Using a new Test Point
• Graph y < 2/5x in a coordinate plane.
• Sketch the boundary line of the graph.
 Find the x- and y-intercept and plot them.
• Use the line’s slope
to graph another point.
y
5
– Solid or dashed line?
• Use a test point
OTHER than the
origin.
• Shade where the
solutions are.
x
-5
-5
5
Example 5:
Let’s Try This!
• Graph y ≥ 3x + 1 in a coordinate plane.
y
x
Example 6:
You Try
• Graph y + 2x < 4 in a coordinate plane.
y
x
Example 7:
You Try
• Graph 2x – 3y ≤ 6 in a coordinate plane.
y
x
Example 8:
You Try
• Graph 2y > x in a coordinate plane.
y
x
Homework
• Inequality Worksheet
–SHOW WORK! 
–GRAPH! 