2.8 – Graph Linear Inequalities in
Two Variables
A linear inequality in two variables can be written in
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 a linear
inequality in two variables if the inequality is true
when the values of x and y are substituted into the
inequality.
2.8 – Graph Linear Inequalities in
Two Variables
Example 1:
Which ordered pair is a solution of 3x + 4y > 8?
a. (6, -3)
b. (0, 2)
c. (-2, -1)
d. (-3, 5)
2.8 – Graph Linear Inequalities in
Two Variables
Example 2:
Which ordered pair is a solution of 5x – 2y < 6?
a. (0, -3)
b. (5, 5)
c. (1, -2)
d. (3, 3)
2.8 – Graph Linear Inequalities in
Two Variables
Example 3:
Tell whether the given ordered pair is a solution
of 5x – 2y < 6.
(0, -4)
(2, 2)
(-3, 8)
(-1, -7)
2.8 – Graph Linear Inequalities in
Two Variables
The graph of a linear inequality in two variables
is the set of all points in a coordinate plane
that represent the solutions of the
inequality.
2.8 – Graph Linear Inequalities in
Two Variables
2.8 – Graph Linear Inequalities in
Two Variables
Example 4:
Graph the following graphs in a coordinate
plane.
a. y < -3
b. x < 2
2.8 – Graph Linear Inequalities in
Two Variables
Example 5:
Graph the following graphs in a coordinate
plane.
a. y > 2x
b. 5x – 2y < -4
2.8 – Graph Linear Inequalities in
Two Variables
Example 6:
Graph the following graphs in a coordinate
plane.
a. y > 2x + 3
b. x + 3y < 9
2.8 – Graph Linear Inequalities in
Two Variables
Example 7:
You have two part-time summer jobs, one that
pays $9 per hour and another that pays
$12 per hour. You would like to earn at
least $240 a week. Write an inequality
describing the possible amounts of time
you can schedule at both jobs. Graph the
inequality. Identify three possible
solutions of the inequality.
2.8 – Graph Linear Inequalities in
Two Variables
Example 8:
Graph y > -2|x – 3| + 4