1. 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

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

3. 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

4. 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.

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.

6. Objective 2
Graph linear inequalities.

7. ) One Variable vs. Two Variables3 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

8. 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

9. 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

10. 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 ≥ True

11. 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

12. Graph: x ≤ 4

13. 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

14. 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

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

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