2.8 Graphing Linear
Inequalities
Algebra 2
Mrs. Spitz
Fall 2006
Objectives
• Draw graphs of inequalities in two
variables, and
• Write an inequality to solve problems.
Assignment
• pp. 94-95#13-28 all
Introduction
• When graphing inequalities, the
boundaries you draw may be solid or
dashed. If the inequality uses the symbol
≥ or ≤ , which may include equality, the
boundary will be solid. Otherwise, it will
be dashed. After graphing the boundary,
you must determine which region is to be
shaded.
Introduction
• Test a point on one side of the line. If the
ordered pair satisfied the inequality, that
region contains solutions to the inequality.
If the ordered pair does not satisfy the
inequality, the other region is the solution.
Chalkboard examples
1. Graph y < 3.
2. Graph y ≤ |x|
Chalkboard examples
1. Graph
1
3
y  x
4
4
2. Graph y < 3x +1
Chalkboard examples
1. Graph y ≥ |x| + 1
2. Graph 3x ≥ 4y
Ex. 1: Graph 2y – 5 ≤ 8.
• The boundary will be
the graph of 2y – 5 =
8. Use x and y
intercepts to graph
the boundary more
easily.
x-intercept
y-intercept
2 y  5x  8
2 y  5x  8
2(0)  5 x  8
2 y  5(0)  8
2y  8
 5x  8
x
8
5
y4
Graph the x and y intercepts on a coordinate graphing plane.
Draw a solid line connecting these two intercepts. This is the
boundary.
Now graph/shade
• Now test a point.
• Try (2,0)
2 y  5x  8
2(0)  5(2)  8
0  10  8
 10  8
The region that contains (2, 0) should be shaded.
Ex. 2: Graph y > |x| - 1.
• The absolute value
has two conditions to
consider
• y > -x – 1
When x < 0
When x ≥ 0
y > -x -1
y > x -1
Graph each inequality for the specified
values of x. The lines will be dashed.
Now graph/shade
• Now test a point.
• Try (0,0)
y | x | 1
0 | 0 | 1
0  1
The region that contains (0, 0) should be shaded.