Algebra 2 Section 1-5

1. Section 1-5 Graphing Linear Inequalities

2. Essential Questions •How do you graph linear inequalities? • How do you apply linear inequalities?

3. Vocabulary 1. Linear Inequality: 2. Boundary: 3. Constraint:

4. Vocabulary 1. Linear Inequality: 2. Boundary: 3. Constraint: Like a linear equation, but with an inequality sign instead of an equal sign; solution set will include a shaded region

5. Vocabulary 1. Linear Inequality: 2. Boundary: 3. Constraint: Like a linear equation, but with an inequality sign instead of an equal sign; solution set will include a shaded region The dashed or solid line at the edge of the shaded region of a linear inequality

6. Vocabulary 1. Linear Inequality: 2. Boundary: 3. Constraint: Like a linear equation, but with an inequality sign instead of an equal sign; solution set will include a shaded region The dashed or solid line at the edge of the shaded region of a linear inequality A condition that the solution of a problem must satisfy

7. Constraints

8. Constraints

9. Constraints Sign Points Boundary Line Shade

10. Constraints Sign Points Boundary Line Shade < Open Dashed Below

11. Constraints Sign Points Boundary Line Shade < Open Dashed Below > Open Dashed Above

12. Constraints Sign Points Boundary Line Shade < Open Dashed Below > Open Dashed Above ≤ Closed Solid Below

13. Constraints Sign Points Boundary Line Shade < Open Dashed Below > Open Dashed Above ≤ Closed Solid Below ≥ Closed Solid Above

14. Example 1 Graph y ≥ −3x + 4

15. Example 1 Graph y ≥ −3x + 4 m = −3

16. Example 1 Graph y ≥ −3x + 4 m = −3 Down 3, right 1

17. Example 1 Graph y ≥ −3x + 4 m = −3 Down 3, right 1 y-intercept: (0, 4)

18. Example 1 Graph y ≥ −3x + 4 m = −3 Down 3, right 1 y-intercept: (0, 4) Closed points

19. Example 1 Graph y ≥ −3x + 4 m = −3 Down 3, right 1 y-intercept: (0, 4) Closed points Solid boundary

20. Example 1 Graph y ≥ −3x + 4 m = −3 Down 3, right 1 y-intercept: (0, 4) Closed points Solid boundary Shade above

21. Example 1 Graph y ≥ −3x + 4 m = −3 Down 3, right 1 y-intercept: (0, 4) x y Closed points Solid boundary Shade above

30. Example 2 Graph x − 2y < 4

31. Example 2 Graph x − 2y < 4 x − 2y < 4

32. Example 2 Graph x − 2y < 4 x − 2y < 4 −2y < −x + 4

33. Example 2 Graph x − 2y < 4 x − 2y < 4 −2y < −x + 4 y > 1 2 x − 2

34. Example 2 Graph x − 2y < 4 m = 1 2 x − 2y < 4 −2y < −x + 4 y > 1 2 x − 2

35. Example 2 Graph x − 2y < 4 m = 1 2 Up 3, right 2 x − 2y < 4 −2y < −x + 4 y > 1 2 x − 2

36. Example 2 Graph x − 2y < 4 m = 1 2 Up 3, right 2 y-intercept: (0, -2) x − 2y < 4 −2y < −x + 4 y > 1 2 x − 2

37. Example 2 Graph x − 2y < 4 m = 1 2 Up 3, right 2 y-intercept: (0, -2) Open points x − 2y < 4 −2y < −x + 4 y > 1 2 x − 2

38. Example 2 Graph x − 2y < 4 m = 1 2 Up 3, right 2 y-intercept: (0, -2) Open points Dashed boundary x − 2y < 4 −2y < −x + 4 y > 1 2 x − 2

39. Example 2 Graph x − 2y < 4 m = 1 2 Up 3, right 2 y-intercept: (0, -2) Open points Dashed boundary Shade above x − 2y < 4 −2y < −x + 4 y > 1 2 x − 2

40. Example 2 Graph x − 2y < 4 m = 1 2 Up 3, right 2 y-intercept: (0, -2) x y Open points Dashed boundary Shade above x − 2y < 4 −2y < −x + 4 y > 1 2 x − 2

52. Example 3 Graph x ≥ −5

53. Example 3 Graph x ≥ −5 m = undeﬁned

54. Example 3 Graph x ≥ −5 Vertical Boundary Line m = undeﬁned

55. Example 3 Graph x ≥ −5 Vertical Boundary Line x-intercept: (-5, 0) m = undeﬁned

56. Example 3 Graph x ≥ −5 Vertical Boundary Line x-intercept: (-5, 0) Closed points m = undeﬁned

57. Example 3 Graph x ≥ −5 Vertical Boundary Line x-intercept: (-5, 0) Closed points Solid boundary m = undeﬁned

58. Example 3 Graph x ≥ −5 Vertical Boundary Line x-intercept: (-5, 0) Closed points Solid boundary Shade right m = undeﬁned

59. Example 3 Graph x ≥ −5 Vertical Boundary Line x-intercept: (-5, 0) x y Closed points Solid boundary Shade right m = undeﬁned

63. Example 4 Shecky’s Tutoring Tutor’s advertises that is specializes in helping student who have a combined SAT verbal and math score of 900 or less. a. Write an inequality to describe the combined scores of students who are prospective tutoring clients. Let x represent the verbal score and y represent the math score.

64. Example 4 Shecky’s Tutoring Tutor’s advertises that is specializes in helping student who have a combined SAT verbal and math score of 900 or less. a. Write an inequality to describe the combined scores of students who are prospective tutoring clients. Let x represent the verbal score and y represent the math score. x + y ≤ 900

65. Example 4 Shecky’s Tutoring Tutor’s advertises that is specializes in helping student who have a combined SAT verbal and math score of 900 or less. b. Does a student with a verbal score of 480 and a math score of 410 ﬁt Shecky’s Tutoring Tutor’s specialty range? Explain.

66. Example 4 Shecky’s Tutoring Tutor’s advertises that is specializes in helping student who have a combined SAT verbal and math score of 900 or less. b. Does a student with a verbal score of 480 and a math score of 410 ﬁt Shecky’s Tutoring Tutor’s specialty range? Explain. 480 + 410 ≤ 900

67. Example 4 Shecky’s Tutoring Tutor’s advertises that is specializes in helping student who have a combined SAT verbal and math score of 900 or less. b. Does a student with a verbal score of 480 and a math score of 410 ﬁt Shecky’s Tutoring Tutor’s specialty range? Explain. 480 + 410 ≤ 900 890 ≤ 900

68. Example 4 Shecky’s Tutoring Tutor’s advertises that is specializes in helping student who have a combined SAT verbal and math score of 900 or less. b. Does a student with a verbal score of 480 and a math score of 410 ﬁt Shecky’s Tutoring Tutor’s specialty range? Explain. 480 + 410 ≤ 900 890 ≤ 900 Yes, the combined score of 890 is less than 900.

Algebra 2 Section 1-5

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Algebra 2 Section 1-5

Similar to Algebra 2 Section 1-5 (20)

More from Jimbo Lamb

More from Jimbo Lamb (20)

Recently uploaded

Recently uploaded (20)

Algebra 2 Section 1-5