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3. 4-1 Understanding Slope

4. Geogebra Finding the Slope of a Line Slopes of Horizontal lines Slopes of Vertical lines Finding Slope From a Table Slope Slope from a Graph Naming Coordinates Boat Game

5. Video Tutor Help Finding slope using rise/run

6. 4-1 Videos Locating and describing the y-intercept of a linear function In this lesson you will learn how to describe the y-intercept of a linear function by examining the four representations of a function. Standards: 8.F.A.3 Describe the rate of change of a linear function In this lesson you will learn how to describe the rate of change in a linear function by using the four representations. Standards: 8.F.A.3 Identify a linear function by analyzing characteristics of a linear f... In this lesson you will learn how to identify a linear function relation by analyzing characteristics of a linear function. Standards: 8.F.A.3

7. Construct linear functions from tables In this lesson you will learn how to construct linear functions from tables. Standards: 8.F.B.4 Construct linear functions from a graph In this lesson you will learn how to construct linear functions from a graph. Standards: 8.F.B.4 Describe positive and negative slopes In this lesson you will learn to describe positive and negative slopes by using directed measurements. Standards: 8.EE.B.6 Derive y=mx using similar triangles In this lesson you will learn to derive the equation y=mx by using similar triangles. Standards: 8.EE.B.6 Derive y=mx+b using similar triangles In this lesson you will learn to derive the equation y=mx+b by using similar triangles. Standards: 8.EE.B.6

8. Determining the constant rate of change In this lesson you will learn calculate the rate of change of a linear function by examining the four representations of a function. Standards: 8.F.B.4 Determining the y-intercept In this lesson you will learn how to determine the initial value of a linear function by interpreting all four representations of a function. Standards: 8.F.B.4 Create equation, table, and graph from a situation In this lesson you will learn how to create an equation, table, and graph by using a contextual situation. Standards: 8.F.B.4 Interpreting slope and y-intercept in context In this lesson you will learn how to interpret the rate of change and the y-intercept in context by examining each of the four representations. Standards: 8.F.B.4 Construct a linear function In this lesson you will learn how to construct a linear function by calculating the slope and y-intercept given any representation. Standards: 8.F.B.4

9. Make lines from right triangles In this lesson you will learn how to make a straight line by using right triangles. Standards: 8.EE.B.6 Find coordinates of points on a straight line In this lesson you will learn to determine coordinates of points on a straight line by using similar triangles. Standards: 8.EE.B.6 Describe a line with a unique slope In this lesson you will learn to describe a straight line by naming its unique slope. Standards: 8.EE.B.6 Find the slope of a line on the coordinate plane In this lesson you will learn to find the slope of a line on a coordinate plane by drawing a right triangle. Standards: 8.EE.B.6

10. Video Tutor Help Slope: graph the line Word problem: rate of change Finding a unit rateFinding a unit rate (Chapter 4) Comparing unit ratesComparing unit rates (Chapter 4) Finding slope using rise/runFinding slope using rise/run (4-1) Understanding Slope Finding the slope of a line Finding Slope From a Table Slope-intercept form Khan Academy 4-1 Understanding Slope Course 3 Slope "Slope" is a fundamental concept in mathematics. Slope is often defined as "the rise over the run"... but why?

11. Make lines from right triangles In this lesson you will learn how to make a straight line by using right triangles. Standards: 8.EE.B.6 Find coordinates of points on a straight line In this lesson you will learn to determine coordinates of points on a straight line by using similar triangles. Standards: 8.EE.B.6 Describe a line with a unique slope In this lesson you will learn to describe a straight line by naming its unique slope. Standards: 8.EE.B.6 Find the slope of a line on the coordinate plane In this lesson you will learn to find the slope of a line on a coordinate plane by drawing a right triangle. Standards: 8.EE.B.6

12. Describe positive and negative slopes In this lesson you will learn to describe positive and negative slopes by using directed measurements. Standards: 8.EE.B.6 Derive y=mx using similar triangles In this lesson you will learn to derive the equation y=mx by using similar triangles. Standards: 8.EE.B.6 Derive y=mx+b using similar triangles In this lesson you will learn to derive the equation y=mx+b by using similar triangles. Standards: 8.EE.B.6

13. Interpret linear relationships in word problems In this lesson you will learn to interpret linear relationships by analyzing word problems. Standards: 8.F.B.4 Interpret direction by analyzing graphs Interpret direction in linear relationships by analyzing graphs Standards: 8.F.B.4 Determine rate of change in linear relationships In this lesson you will learn to determine rate of change in linear relationships by comparing slopes in a graph. Standards: 8.F.B.4 Determine initial value in a linear relationship In this lesson you will learn to interpret the initial value in a linear relationship by analyzing graphs. Standards: 8.F.B.4

14. Define and interpret linear relationships in tables In this lesson you will learn to define and interpret linear relationships by analyzing tables. Standards: 8.F.B.4 Define a linear function In this lesson you will learn to define a linear function by constructing an equation. Standards: 8.F.B.4 Construct a function by solving for unknown information In this lesson you will learn to construct a linear function by solving for unknown information. Standards: 8.F.B.4

15. Determining the constant rate of change In this lesson you will learn calculate the rate of change of a linear function by examining the four representations of a function. Standards: 8.F.B.4 Determining the y-intercept In this lesson you will learn how to determine the initial value of a linear function by interpreting all four representations of a function. Standards: 8.F.B.4 Create equation, table, and graph from a situation In this lesson you will learn how to create an equation, table, and graph by using a contextual situation. Standards: 8.F.B.4 Interpreting slope and y-intercept in context In this lesson you will learn how to interpret the rate of change and the y-intercept in context by examining each of the four representations. Standards: 8.F.B.4 Construct a linear function In this lesson you will learn how to construct a linear function by calculating the slope and y-intercept given any representation. Standards: 8.F.B.4

16. Compare distance-time graphs with distance-time equations In this lesson you will learn how to compare distance-time graphs with distance- time equations. Standards: 8.F.A.2 Construct linear functions from tables In this lesson you will learn how to construct linear functions from tables. Standards: 8.F.B.4 Construct linear functions from a graph In this lesson you will learn how to construct linear functions from a graph. Standards: 8.F.B.4

17. Worksheets 4-1 Note-Taking Guide 4-1Practice 4-1 Guided Problem Solving

18. Vocabulary Practice Chapter 4 Vocabulary (Electronic) Flash Cards

19. Additional Lesson Examples 4-1 Step-by-Step Examples

20. Lesson Readiness 4-1 Problem of the Day 4-1 Lesson Quiz

23. Naming Coordinates Boat Game

24. Finding the slope of a line…

25. What is the meaning of this sign? 1.Icy Road Ahead 2.Steep Road Ahead 3.Curvy Road Ahead 4.Trucks Entering Highway Ahead

26. What does the 7% mean? 7% is the slope of the road. It means the road drops 7 feet vertically for every 100 feet horizontally. 7% So, what is slope??? Slope is the steepness of a line. 7 feet 100 feet

33. Slope from a Graph Slope Finding the Slope of a Line

44. Slopes of Horizontal lines

46. Slopes of Vertical lines

54. Slope You can find the slope of a line by using the coordinates of any two points on the line. One point can be represented by (x 1, y 1 ) and the other by (x 2, y 2 ). The small numbers slightly below x and y are called subscripts.

55. Slope Formula The slope m of a line passing through points (x 1, y 1 ) and (x 2, y 2 ) is the ratio of the difference in the y-coordinates to the corresponding difference in the x-coordinates. Where x 2 ≠ x 1 (x 1, y 1 ) (x 2, y 2 ) m = y 2 – y 1 x 2 – x 1

56. Study Tip It does not matter which point you define as and. However, the coordinates of both points must be used in the same order. (x 1, y 1 ) (x 2, y 2 )

58. Example 4-1a Find the slope of the line that passes through A(3, 3) and B(2, 0). Simplify. Definition of slope Positive Slope

59. Example 4-1b Check When going from left to right, the graph of the line slants upward. This is consistent with a positive slope. Answer: The slope is 3.

60. Example 4-2a Find the slope of the line that passes through X(–2, 3) and Y(3, 0). Definition of slope Simplify. Negative Slope

61. Example 4-2b Check When going from left to right, the graph of the line slants downward. This is consistent with a negative slope. Answer: The slope is.

62. Example 4-3a Find the slope of the line that passes through P(6, 5) and Q(2, 5). Definition of slope Simplify. Zero Slope

63. Example 4-3b Answer: The slope is 0. The slope of any horizontal line is 0.

64. Example 4-4a Find the slope of the line that passes through G(2, 4) and H(2, 6). Definition of slope Simplify. Undefined Slope

65. Example 4-4b Answer: Division by 0 is not defined. So, the slope is undefined. The slope of any vertical line is undefined.

66. Example 4-1a Find the slope of a hill that rises 30 feet for every horizontal change of 150 feet. Definition of slope rise = 30 feet, run = 150 feet Simplify. Answer: The slope of the hill isor 0.2. Use Rise and Run to Find Slope

67. Example 4-1b Find the slope of a hill that rises 40 feet for every horizontal change of 100 feet. Answer:

68. Example 4-2a Find the slope of the line. Definition of slope Answer: The slope is 3. Positive Slope

69. Example 4-2b Find the slope of the line. Answer:

70. Example 4-3a Find the slope of the line. Answer: The slope is. Definition of slope Negative Slope

71. Example 4-3b Find the slope of the line. Answer:

72. Example 4-4a Find the slope of the line. Answer: The slope is 0. Definition of slope Zero Slope

73. Example 4-4b Find the slope of the line. Answer: 0

74. Example 4-5a Find the slope of the line. Answer: The slope is undefined. Division by 0 is undefined. So, the slope is undefined. Undefined Slope

75. Example 4-5b Find the slope of the line. Answer: undefined

76. Understanding Slope LESSON 4-1 Using coordinates, find the slope of the line between P (–2, 3) and Q (–1, –1). 3 – (–1) –2 – (–1) = Subtract the coordinates of point Q from the coordinates of point P. slope = change in y change in x Simplify. = or –4 4– 14– 1 Additional Examples

78. Understanding Slope LESSON 4-1 Find the slope of each line. State whether the slope is zero or undefined. a. line k Division by zero is undefined. The slope of a vertical line is undefined. b. line p The slope of a horizontal line is zero. slope = = = 0 2 – 2 –2 – 3 0 –5 slope = = 1 – (–3) 2 – 2 4040 Additional Examples

80. Understanding Slope Graph the distance-cost data below. Connect the points with a line. Then find the rate of change. LESSON 4-1 Distance (mi)0100200 300 400 500 Cost ($)025 50 75 100 125 The amount spent on fuel increases $1 for every 4 miles driven. rate of Change Use coordinates of two points. change in y change in x = slope 25 – 0 100 – 0 == Subtract and simplify. 25 100 = 1414 = Additional Examples Finding Slope From a Table

83. Partner Share! Example 2 The table shows the total cost of gas per gallon. Use the data to make a graph. Find the slope of the line and explain what it shows. Graph the data. Cost of Gas GallonsCost 00 36 612 6 9 9 6 0 3 3 x y Gallons Cost of Gas Cost

84. Partner Share! Example 2 Continued Find the slope of the line: The slope of the line is 2. This means that for every gallon of gas, you will pay another $2. = y 2 – y 1 x 2 – x 1 6 3 12  6 6  3 = 2 6 9 9 12 6 0 3 3 x y Gallons Cost of Gas Cost Substitute. Divide.

85. The slope of a line may be positive, negative, zero, or undefined. You can tell which of these is the case by looking at the graphs of a line— you do not need to calculate the slope.

88. Lesson Review: Part I Find the slope of the line that passes through each pair of points. 1. (4, 3) and (–1, 1) 2. (–1, 5) and (4, 2) 2 55 3 –

89. Lesson Review: Part II 3. The table shows how much money Susan earned as a house painter for one afternoon. Use the data to make a graph. Find the slope of the line and explain what it shows. x y 64 2 8 101214 0 10 20 30 40 50 60 70 80 The slope of the line is 7. This means Susan earned $7 for each hour worked.