1. Graphing Linear Inequalities

2. Objectives How do we graph an inequality Define a boundary line Graphing a boundary line Define the solution for an inequality

3. What is the solution of an inequality Solution of an inequality are all the ordered pairs (points) that make the inequality true.

4. Graphing Inequalities Consider the inequality y ≥ x 6 4 2 2 14365 1 3 5 y = xGraph Boundary line REMEMBER: Solution are all the ordered pairs (points) that make the inequality true.

5. Graphing Inequalities Consider the inequality y ≥ x 6 4 2 2 14365 1 3 5 1.Pick two points from each side of the graph (4,1) (1,3)

6. Graphing Inequalities Consider the inequality y ≥ x 6 4 2 2 14365 1 3 5 (4,1) (1,3) 2.Check points if they make inequality true. (1,3)y ≥ x substitute into

7. Graphing Inequalities Consider the inequality y ≥ x 6 4 2 2 14365 1 3 5 (4,1) (1,3) 2.Check points if they make inequality true. (1,3)(1,3)y ≥ x substitute into 3 ≥ 1

8. Graphing Inequalities Consider the inequality y ≥ x 6 4 2 2 14365 1 3 5 (4,1) (1,3) 2.Check points if they make inequality true. (1,3)(1,3)y ≥ x substitute into 3 ≥ 1  

9. Graphing Inequalities Consider the inequality y ≥ x 6 4 2 2 14365 1 3 5 (4,1) (1,3) 2.Check points if they make inequality true. (4,1)y ≥ x substitute into 

10. Graphing Inequalities Consider the inequality y ≥ x 6 4 2 2 14365 1 3 5 (4,1) (1,3) 2.Check points if they make inequality true. (4,1)(4,1)y ≥ x substitute into  1 ≥ 4

11. Graphing Inequalities Consider the inequality y ≥ x 6 4 2 2 14365 1 3 5 (4,1) (1,3) 2.Check points if they make inequality true. (4,1)(4,1)y ≥ x substitute into  1 ≥ 4X X

12. Graphing Inequalities Consider the inequality y ≥ x 6 4 2 2 14365 1 3 5 (4,1) (1,3) 3.Shade the side where the correct point lies.  X

13. Graphing Inequalities Consider the inequality y ≥ x 6 4 2 2 14365 1 3 5 (1,3) 3.Shade the side where the correct point lies. 

14. Graphing Inequalities Consider the inequality x - 2y < 4 3 1 2 14365 -2 2 x - 2y = 4Graph y > x - 2 1 2

15. Graphing Inequalities Consider the inequality x - 2y < 4 3 1 2 14365 -2 2 x - 2y = 4Graph ??TEST POINTS ?? Is there an easier way??? (0,1) (6,0) y > x - 2 1 2

16. Graphing Inequalities Consider the inequality x - 2y < 4 3 1 2 14365 -2 2 YES!!!!! y > x - 2 1 2

17. Graphing Inequalities Consider the inequality x - 2y < 4 3 1 2 14365 -2 2 I've already graphed the "or equal to" part (it's just the line); now I'm ready to do the "y greater than" part. y > x - 2 1 2

18. Graphing Inequalities Consider the inequality x - 2y < 4 3 1 2 14365 -2 2 In other words, this is where I need to shade one side of the line or the other. y > x - 2 1 2 Hidden word: vegetable

19. Graphing Inequalities Consider the inequality x - 2y < 4 3 1 2 14365 -2 2 Now think about it: y > x - 2 1 2

20. Graphing Inequalities Consider the inequality x - 2y < 4 3 1 2 14365 -2 2 If I need y GREATER THAN the line, do I want ABOVE the line, or BELOW? y > x - 2 1 2

21. Graphing Inequalities Consider the inequality x - 2y < 4 3 1 2 14365 -2 2 Naturally, I want above the line. So I shade it in: y > x - 2 1 2

22. Graphing Inequalities Consider the inequality x - 2y < 4 3 1 2 14365 -2 2 (0,1) (6,0)  X ¡¡ SHADE CORRECT REGION !!

23. Examples 6 4 2 2 14365 1 3 5 3y - 2x ≥ 9 1. y = x + 3 2 3 GRAPH

24. Examples 6 4 2 2 14365 1 3 5 3y - 2x ≥ 9 1. y ≥ x + 3 2 3 GRAPH Which side did you shade?

25. Examples 2. x - 3y > -3 y < x + 1 1 3 6 4 2 2 14365 1 3 5 Graph Did you remember to “dash the line”

26. Examples 2. x - 3y > -3 y < x + 1 1 3 6 4 2 2 14365 1 3 5 Graph Which side did you shade?

27. Solving a system of Inequalities Consider the system x + y ≥ -1 -2x + y < 2 3 1 2 13 2 -2-3

28. Solving a system of Inequalities Consider the system x + y ≥ -1 -2x + y < 2 3 1 2 13 2 -2-3 y≥-x-1

29. Now you try When you have finished the work make sure to fill out a 3-2-1 document. Find the hidden word with in the power point and write it next to your name.