1. Section 7.1
Graphs, Slopes, Inequalities and Applications

2. OBJECTIVES
Find and graph an equation of a line given its slope and a point on the line. A

3. OBJECTIVES
Find and graph an equation of a line given its slope and y-intercept. B

4. OBJECTIVES
Find and graph an equation of a line given two points on that line. C

5. DEFINITION Point-slope form
The point-slope form of the equation of the line going through ( ), and having slope m is

6. DEFINITION Slope-intercept form
The slope-intercept form of the equation of the line having slope m and y-intercept b is

7. PROCEDURE
Finding the Equation of a Line

8. PROCEDURE
Finding the Equation of a Line

9. PROCEDURE
Finding the Equation of a Line

10. PROCEDURE
Finding the Equation of a Line

11. NOTE
The Resulting Equation Can Always Be Written as
Ax + By = C

12. Section 7.1 Exercise #1 Chapter
Graphs, Slopes, Inequalities and Applications
Section 7.1 Exercise #1
Let’s work Exercise #19 from Section 5.1

13. Let’s work Exercise #19 from Section 5.1

14. (1,– 1)
(2,– 6)
Let’s work Exercise #19 from Section 5.1

15. Section 7.1 Exercise #2 Chapter 7
Graphs, Slopes, Inequalities and Applications
Section 7.1 Exercise #2
Let’s work Exercise #19 from Section 5.1

16. Let’s work Exercise #19 from Section 5.1

17. (1, 1)
(0, – 4)
Let’s work Exercise #19 from Section 5.1

18. Section 7.1 Exercise #3 Chapter 7
Graphs, Slopes, Inequalities and Applications
Section 7.1 Exercise #3
Let’s work Exercise #19 from Section 5.1

19. Let’s work Exercise #19 from Section 5.1

20. Let’s work Exercise #19 from Section 5.1

21. Section 7.2
Graphs, Slopes, Inequalities and Applications

22. OBJECTIVES
Solve applications involving the point-slope formula. A

23. OBJECTIVES
Solve applications involving the slope-intercept formula. B

24. OBJECTIVES
Solve applications involving the two-point formula. C

25. Section 7.2 Exercise #4 Chapter 7
Graphs, Slopes, Inequalities and Applications
Section 7.2 Exercise #4
Let’s work Exercise #19 from Section 5.1

26. Long-distance rates for m minutes are $10 plus $0.20 for
each minute. If a 10-minute call costs $12, write an
equation for the total cost C and find the cost of a
15-minute call.
Step 1: Read the problem.
Step 2: Select the unknown.
Let’s work Exercise #19 from Section 5.1
Step 3: Translate.

27. Long-distance rates for m minutes are $10 plus $0.20 for
each minute. If a 10-minute call costs $12, write an
equation for the total cost C and find the cost of a
15-minute call.
Step 4: Use Algebra to find the cost C of an m = 15 minute call.
Let’s work Exercise #19 from Section 5.1

28. Section 7.2 Exercise #5 Chapter 7
Graphs, Slopes, Inequalities and Applications
Section 7.2 Exercise #5
Let’s work Exercise #19 from Section 5.1

29. m minutes are used after the first 500. What is
A cell phone plan costs $40 per month with 500 free minutes and $0.50 for each additional minute. Find an equation for the total cost C of the plan when
m minutes are used after the first 500. What is
the cost when 800 total minutes are used?
Step 1: Read the problem.
Step 2: Select the unknown.
Let’s work Exercise #19 from Section 5.1
Step 3: Translate.

30. m minutes are used after the first 500. What is
A cell phone plan costs $40 per month with 500 free minutes and $0.50 for each additional minute. Find an equation for the total cost C of the plan when
m minutes are used after the first 500. What is
the cost when 800 total minutes are used?
Step 4: Use Algebra to find the cost C when 800 minutes are used.
Let’s work Exercise #19 from Section 5.1

31. m minutes are used after the first 500. What is
A cell phone plan costs $40 per month with 500 free minutes and $0.50 for each additional minute. Find an equation for the total cost C of the plan when
m minutes are used after the first 500. What is
the cost when 800 total minutes are used?
Let’s work Exercise #19 from Section 5.1

32. Section 7.3
Graphs, Slopes, Inequalities and Applications

33. OBJECTIVES
Graph linear inequalities in two variables. A

34. PROCEDURE
Graphing a Linear Inequality

35. PROCEDURE
Graphing a Linear Inequality

36. PROCEDURE Graphing a Linear Inequality Use any point (a, b)
as a test point.
Substitute the values of a and b for x and y in the inequality.

37. PROCEDURE Graphing a Linear Inequality
If a true statement results, shade the side of the line containing the test point.
If a false statement results, shade the other side.

38. Section 7.3 Exercise #7 Chapter 7
Graphs, Slopes, Inequalities and Applications
Section 7.3 Exercise #7
Let’s work Exercise #19 from Section 5.1

39. Let’s work Exercise #19 from Section 5.1

40. Section 7.3 Exercise #8 Chapter 7
Graphs, Slopes, Inequalities and Applications
Section 7.3 Exercise #8
Let’s work Exercise #19 from Section 5.1

41. Let’s work Exercise #19 from Section 5.1

42. Section 7.3 Exercise #9 Chapter 7
Graphs, Slopes, Inequalities and Applications
Section 7.3 Exercise #9
Let’s work Exercise #19 from Section 5.1

43. Let’s work Exercise #19 from Section 5.1

44. Section 7.3 Exercise #10 Chapter 7
Graphs, Slopes, Inequalities and Applications
Section 7.3 Exercise #10
Let’s work Exercise #19 from Section 5.1

45. Let’s work Exercise #19 from Section 5.1

46. Section 7.3 Exercise #12 Chapter 7
Graphs, Slopes, Inequalities and Applications
Section 7.3 Exercise #12
Let’s work Exercise #19 from Section 5.1

47. Step 1: Read the problem.
Let’s work Exercise #19 from Section 5.1

48. Step 2: Select the unknown.

49. Step 3: Translate.

50. Step 4: Use Algebra

51. Section 7.4
Graphs, Slopes, Inequalities and Applications

52. OBJECTIVES
Find and solve equations of direct variation given values of the variables. A

53. OBJECTIVES
Find and solve equations of inverse variation given values of the variables. B

54. OBJECTIVES
Solve applications involving variation. C

55. DEFINITION y varies directly as x if
There is a constant k such that y = kx
k is the constant of variation or proportionality.

56. Section 7.4 Exercise #11 Chapter 7
Graphs, Slopes, Inequalities and Applications
Section 7.4 Exercise #11
Let’s work Exercise #19 from Section 5.1

57. Step 2: Select the unknown.
Step 1: Read the problem.
Step 2: Select the unknown.
Let’s work Exercise #19 from Section 5.1

58. Step 3: Translate.

59. Step 4: Use Algebra