1. 2.8 – Graphing Inequalities

2. Steps for graphing inequalities:

3. 2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation:

4. 2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table

5. 2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form

6. 2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts

7. 2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form

8. 2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid.

9. 2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed.

10. 2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality.

11. 2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality.  Plug 0 in for x and plug 0 in for y!

12. 2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality.  Plug 0 in for x and plug 0 in for y!

13. 2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality.  Plug 0 in for x and plug 0 in for y!  If true, shade side of line with the origin.

14. 2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality.  Plug 0 in for x and plug 0 in for y!  If true, shade side of line with the origin.

15. 2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality.  Plug 0 in for x and plug 0 in for y!  If true, shade side of line with the origin.  If false, shade side of line w/o the origin.

16. 2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality.  Plug 0 in for x and plug 0 in for y!  If true, shade side of line with the origin.  If false, shade side of line w/o the origin.

17. Ex. 1 Graph 2x + 3y > 6

18. 1)Graph just like the equation:

19. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6

20. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int:

21. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0)

22. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int:

23. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2)

24. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2)

25. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2)

26. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid.

27. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed.

28. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed.

29. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed.

30. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality.

31. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality. Plug 0 in for x and plug 0 in for y!

32. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality. Plug 0 in for x and plug 0 in for y! 2(0) + 3(0) > 6

33. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality. Plug 0 in for x and plug 0 in for y! 2(0) + 3(0) > 6 0 > 6

34. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality. Plug 0 in for x and plug 0 in for y! 2(0) + 3(0) > 6 0 > 6 If true, shade side of line with the origin.

35. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality. Plug 0 in for x and plug 0 in for y! 2(0) + 3(0) > 6 0 > 6 If true, shade side of line with the origin. If false, shade side of line w/o the origin.

36. Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality. Plug 0 in for x and plug 0 in for y! 2(0) + 3(0) > 6 0 > 6 If true, shade side of line with the origin. If false, shade side of line w/o the origin.

37. Ex. 2 Graph y ≤ x + 1

38. 1)Graph y = x + 1

39. Ex. 2 Graph y ≤ x + 1 1)Graph y = x + 1 xx + 1y(x,y) -1 + 1-2(-1,0) 00 + 1(0,1) 11 + 10(1,2)

40. Ex. 2 Graph y ≤ x + 1 1)Graph y = x + 1 xx + 1y(x,y) -1 + 1-2(-1,0) 00 + 1(0,1) 11 + 10(1,2)

41. Ex. 2 Graph y ≤ x + 1 1)Graph y = x + 1 2)y ≤ x + 1, so use solid line! xx + 1y(x,y) -1 + 1-2(-1,0) 00 + 1(0,1) 11 + 10(1,2)

42. Ex. 2 Graph y ≤ x + 1 1)Graph y = x + 1 2)y ≤ x + 1, so use solid line! xx + 1y(x,y) -1 + 1-2(-1,0) 00 + 1(0,1) 11 + 10(1,2)

43. Ex. 2 Graph y ≤ x + 1 1)Graph y = x + 1 2)y ≤ x + 1, so use solid line! 3)Plug in the origin: 0 ≤ 0 + 1 0 ≤ 1, TRUE! xx + 1y(x,y) -1 + 1-2(-1,0) 00 + 1(0,1) 11 + 10(1,2)

44. Ex. 2 Graph y ≤ x + 1 1)Graph y = x + 1 2)y ≤ x + 1, so use solid line! 3)Plug in the origin: 0 ≤ 0 + 1 0 ≤ 1, TRUE! xx + 1y(x,y) -1 + 1-2(-1,0) 00 + 1(0,1) 11 + 10(1,2)