4 6 Graphing Linear Inequalities 1 Determine whether

4. 6 Graphing Linear Inequalities 1. Determine whether an ordered pair is a solution for a linear inequality with two variables. 2. Graph linear inequalities. 3 x - 2 y ≤ 6

Objective 1 Determine whether an ordered pair is a solution for a linear inequality with two variables.

Checking an Ordered Pair 1. Replace the variables with the corresponding values 2. Is the inequality true? Yes: the point is a solution No: the point is not a solution

Is (3, – 5) a solution for y 3 x + 4 – 5 3(3) + 4 – 5 9 + 4 – 5 13 Replace x with 3 and y with 5. This statement is true, so (3, – 5) is a solution.

Is (-1, 1) a solution for y > -x + 2. 1 > -(-1) + 2 1>1+2 1>3 This statement is false, so (-1, 1) is not a solution.

Objective 2 Graph linear inequalities.

One Variable vs. Two Variables ) 3 3 When an equation in one variable is solved the answer is a point on a line. Ax + By = C < or > use dotted line Ax + By < C ≤ or ≥ use solid line

To Graph Linear Inequalities 1. Graph the related equation. or draw a solid line < or > draw a dashed line 2. Test Point: True: shade the side with the test point False: shade the side opposite the test point

Graph: y > 4 x + 1 Graph the related equation y = 4 x + 1 (0, 1) m=4 Line: > = Dotted Test point: (0, 0) y > 4 x + 1 0 > 4(0) + 1 0 > 1 False Shade other side of the boundary line.

Graph: x - 4 y ≥ - 8 Graph the related equation x – 4 y = -8 (0, 2) (-8, 0) Line: ≥ = solid Test point: (0, 0) 0 – 0 ≥ -8 True

Graph: 3 x – 4 y < 0 Graph the related equation 3 x – 4 y = 0 (0, 0) m = 3/4 Line: < = dotted Test point: (2, -2) 3(2) – 4(-2) < 0 6+8<0 False

Graph: x≤ 4

Which point is a solution to the inequality 3 x + 2 y 12? a) (0, 3) b) (0, 0) c) (2, 5) d) ( 4, 5) Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4 - 13

Which point is a solution to the inequality 3 x + 2 y 12? a) (0, 3) b) (0, 0) c) (2, 5) d) ( 4, 5) Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4 - 14

Graph 2 x + 3 y 12. a) b) c) d) Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4 - 15

Graph 2 x + 3 y 12. a) b) c) d) Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4 - 16