2-8: Graphing Inequalities
in the Coordinate Plane
Algebra 2 CP
Graphing Inequalities in the Coordinate Plane
When a line is drawn in a plane, the line
separates the plane into __________
distinct
two
regions called ________________.
half-planes
 The line itself is the ________________
of the
boundary
two regions.
 The boundary does __________
belong in either
not
half plane.

half-plane
half-plane
Example 1:
When graphing an
inequality, follow
these steps:
1. Graph the boundary
line – either dashed or
solid.
Graph
y > 2x + 7
Test (0, 0)
y > 2x + 7
0>0+7
2. Select a point (not on
the line) from each half
plane.
3. Shade the half plane
that satisfies the
equation or plot points if
it is a discrete situation.
Test (-4, 0)
y > 2x + 7
0 > -8 + 7
0 > -1
Example 2:
When graphing an
inequality, follow
these steps:
1. Graph the boundary
line – either dashed or
solid.
2. Select a point (not on
the line) from each half
plane.
3. Shade the half plane
that satisfies the
equation or plot points if
it is a discrete situation.
Graph
y  -3x - 2
Test (0, 0)
y ≤ -3x - 2
0≤0-2
0≤-2
Test (-4, 0)
y ≤ -3x - 2
0 ≤ 12 - 2
0 ≤ 10
Example 3: You put up a new shelf that is 1 ft. wide to store some of your books
and trophies. Each book takes up 1 in. and each trophy takes up 3 in. what is a
graph showing how many books and how many trophies will fit on the shelf?

Relate
# of Books
Define
B = # of Books
Write
# of Trophies
T = # of Trophies

B
 12

3T
12
Find the intercepts of the boundary line and graph the boundary line.
When T  0: B  3  0  12
B  12
When B  0 : 0  3T  12
T 4
Trophies
4
2
2
4
6
Books
8
10
12
Trophies
4
2
2
4
6
Books
2
2
8
10
12
Discrete Graph
This is a __________________
so the shaded region really
represents all the points for
the ___________________
Whole Number
possibilities.
Because you can’t have half
a book or trophy.
Graphing an Absolute Value Inequality
Graph y 1  x  2
When graphing an
Absolute Value
inequality, follow
these steps:
1. Solve the inequality for y
2. Graph the boundary line
– either dashed or solid.
3. Select a point (not on
the line) from each half
plane.
4. Shade the solution
y  x  2 1
Test (0, 0)
Test (0, 4)
0  0  2 1
4  0  2 1
0  2 1
03
4  2 1
43
4
2
2
4
What Inequality Does This Graph Represent?
4
2
2
4
1. How is the vertex translated?
From (0, 0) to (2, 1)
2. Is the solution above or
below the boundary line?
It is above so the inequality is
either > or ≥.
3. Is the boundary line dashed
or solid?
It is dashed so the inequality is >.
y  x  2 1
Homework: p. 118 #9, 11, 15-21 odd, 31, 33,
40-44 even, 56-70 even