Topic 3. Mrs. Daniel- Algebra 1

Transcription

1 Topic 3 Mrs. Daniel- Algebra 1

2 Table of Contents 5.1: Understanding Linear Functions 5.2: Using Intercepts 5.3: Interpreting Rates of Change and Slope 6.1: Slope-Intercept Form 6.2: Point-Slope Form 6.3: Standard Form 6.4 Transforming Linear Functions 6.5: Comparing Properties of Linear Functions

3 Lesson 5.1: Understanding Linear Functions Essential Question: What is a linear function? Pg. 202

4 Standard Form A linear equation is any equation that can be written in the standard from: Ax +By = C, where A, B and C are real numbers and A and B are both not 0.

5

6

7 Discrete vs. Continuous Function

8 Discrete or Continuous? Domain: Range:

9

10 Discrete or Continuous? Domain: Range:

11

12

13 5.2: Using Intercepts Essential Questions: How can you identify and use intercepts in linear relationships? Page: 211

14

15 Vocab: Intercepts X-intercept: y-coordinate of the point where the graph intercepts the y-axis. The x-coordinate of this point is always zero. Y-intercept: x- coordinate of the point where the graph intercepts the x-axis. The y-coordinate of the point is always zero.

16 Find the Intercepts To find x-intercept, replace y with zero and solve for x. To find y-intercept, replace x with zero and solve for y.

17 Find Intercepts: -5x + 6y = 60

18

19

20

21

22

23 Graph Using the Intercepts: 18y = 12x + 108

24 Graph Using the Intercepts: 3y = -5x -3

25

26 5.3: Interpreting Rate of Change and Slope Essential Question: How can you relate rate of change and slope in a linear equation?

27 What is Slope? Slope: describes the steepness or incline of a line. A higher slope value indicates a steeper incline. Slopes can be positive, negative, zero or undefined. Slope is abbreviated with m

28 Determining Slope Graphically We can count the rise and run on a graph to determine slope.

29

30

31 Slope

32 Slope Formula

33 Find the Slope, using the graph

34 Find the Slope, using the table

35

36 Slope: Interpret:

37 Slope: Interpret:

38 Slope: Interpret: Slope: Interpret:

39

40

41

42

43 6.1: Slope Intercept Form Essential Question: How can you represent a linear function in a way that reveals in slopes and y-intercept?

44 Slope Intercept Form

45 Find the slope- intercept form Slope is 3, and (2, 5) is on the line

46 Find the slope- intercept form The line passes through (0,5) and (2,13).

47

48 Graphing the Slope Intercept Form of a Line

49 Graphing the Equation of a Line 1. Start at b. 2. Move up/down 3. Move left/right 4. Repeat

50 Graph: y = 5x -4

51 Graph: 2x + 6y = 6

52 Graph: 2x + 3y = 6

53 Graph: 2x + y = 4

54 Slope: Interpret: Y-intercept: Interpret: Equation:

55 Slope: Interpret: Y-intercept: Interpret: Equation:

56 Lesson 6.2: Point-Slope Form Essential Question: How can you represent a linear equation in a way that it reveals its point and slope on its graph? Pg. 249

57 Point Slope Equation

58 Write the Point-Slope Equation 1. Slope is 3.5 and (-3, 2) is on the line. 2. Slope is 0 and (-2, -1) is on the line.

59

60 Using Point-Slope Solve Paul wants to place an ad in a newspaper. The newspaper charges $10 for the first 2 lines of text and $3 for each additional line of text. Paul s is 8 lines long. How much will the ad cost?

61 Using Point-Slope Solve Paul would like to shop for the best price to place the ad. A different newspaper has a base cost of $15 for 3 lines and $2 for every extra line. How much will an 8-line ad cost in this paper?

62

63 Let s Practice (2, 1) and (3, 4) are on the line. Write an equation in pointslope form.

64 Let s Practice (1, 3) and (2, 3) are on the line. Write an equation in pointslope form.

65

66

67

68

69 Lesson 6.3: Standard Form Essential Question: How can you write a linear equation in Standard Form given properties of the line including its slopes and points on the line? Pg. 261

70 Comparing Forms of Linear Equations

71 Write in Standard Form Slope is 2 and (-2, 2) is on the line.

72 Write in Standard Form Slope is 5 and (-2, 4) is on the line.

73 Let s Practice

74 Write in Standard Form (-2, -1) and (0, 4) are on the line.

75 Write in Standard Form (5, 2) and (3, -6) are on the line.

76 Let s Practice

77 Modeling: Write an Equation in Standard Form A tank is filling up with water at a rate of 3 gallons per minute. The tank already had 3 gallons in it before it started being filled.

78 Modeling: Write an Equation in Standard Form A hot tub filled with 440 gallons of water is being drained. After 1.5 hours, the amount of water had decreased to 320 gallons.

79 Let s Practice

80 Lesson 6.4: Transforming Linear Functions Essential Question: What are the ways in which you can transform the graph of a linear function?

81 What happens when. A. The gym lowers the one time fee to join? B. The gym increased the monthly fee?

82

83 Changes to Words Visually Slope (m) Intercept (b)

84

85

86

87 Lesson 6.5: Comparing Properties of Linear Functions Essential Question: How can you compare linear functions that are represented in different ways?

88 Comparing 2 Functions The domain of each function is the set of all real numbers x such that 5 x 8. The table show some ordered pairs for f(x). The function g(x) is defined by the rule g(x) = 3x + 7. What is the f(x) function rule? f(x) initial value? g(x) initial value? f(x) range? g(x) range?

89 Comparing 2 Functions The domain of each function is the set of all real numbers x such that 6 x 10. The table show some ordered pairs for f(x). The function g(x) is defined by the rule g(x) = 5x What is the f(x) function rule? f(x) initial value? g(x) initial value? f(x) range? g(x) range?

90 Write a function rule for each, and then compare their domain, range, slope and y-intercept. A rainstorm in Austin lasted 3.5 hours, during which time it rained at a steady rate of 4.5 mm per hour. The graph shows the amount of rain that dell during the same rainstorm in Dallas, D(t) as a function of time. Function Rule Austin Dallas Domain Range Slope Y-intercept

91 Write a function rule for each, and then compare their domain, range, slope and y-intercept. The first group of hikers hiked at steady rate of 6.5 km per hour for 4 hours. The graph shows the 2 nd group of hikers. Function Rule 1 st Group 2 nd Group Domain Range Slope Y-intercept

92

93

94

95