Graphing Linear Inequalities 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. 3x - 2y ≤ 6

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

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

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

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 Ax + By < C < or > use dotted line ≤ 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 the related equation y = 4x + 1 Line: Test point: (0, 0) Graph: y > 4x + 1 Graph the related equation y = 4x + 1 Line: Test point: (0, 0) y > 4x + 1 0 > 4(0) + 1 0 > 1 False Shade other side of the boundary line. (0,1) m = 4 > = Dotted

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

Graph the related equation Graph: 3x – 4y < 0 Graph the related equation 3x – 4y = 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 3x + 2y  12? b) (0, 0) c) (2, 5) d) (4, 5) Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

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

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

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