ALGEBRA 1 CCGraphing Linear Inequalities

Example 1• Which ordered pairs are solutions to the inequality:

6x – 2y < 24

a) (4, -1)

b) (0, 3)

c) (-4, -24)

d) (8.5, 2.3)

• Linear Equation:

• Linear Inequality:

• When you have an inequality with one variable, graph on a number line.

• Two variables: Graph on a coordinate plane.

2 4 12

2 4 12

x y

x y

Boundary Line – Divides the coordinate plane into two halves.

Use a solid line.

Use a dotted line.

or

or

How to graph inequalities?

• 1) Graph the boundary line.

Dotted: > or < Solid: ≥ or ≤

• 2) Pick an ordered pair on either side of the boundary line, i.e. (0, 0). Substitute. If the inequality is true, shade that side. If not, shade the other side.

Example 2• Graph 2x + 3y ≥ 6

Example 3• Graph y < 2x

Example 4• Graph x ≥ -3

Example 5• Graph y < 4

Example 6• In the last quarter of a high school basketball game, your

team is behind by 20 points. A field goal is 2 points and a foul shot is 1 point. The coach doesn’t want the team shooting any 3-point shots. Let x represent the number of field goals scored. Let y represent the number of foul shots scored. Write and graph an inequality that models the different numbers of field goals and foul shots your team could score to win or tie the game. (Assume that the other team scores no more points.)

Example 6 (continued)