2.8 – Graph Linear Inequalities in Two Variables

A linear inequality in two variables can be written in one of these forms:

Ax + By < CAx + By < CAx + By > CAx + 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