The document provides examples and explanations of key concepts related to linear functions in slope-intercept form (y = mx + b). It includes examples of finding the slope and y-intercept from graphs, equations, and point pairs. Practice problems are provided for students to identify slopes, match equations to graphs, find the equation from two points, and determine if a relationship represents a function.

1. Jeudi 23 Septembre Warm up A tennis club membership costs $5 a year. In addition to this flat fee, you must pay $2 every time you reserve a court. Which function rule describes the cost (y) for the number of times you reserve a court(x) A. y = 7 B. y = 5x + 2 C. y = 7x D. y = 2x + 5

2. x y 0 1 2 3 y = 2x + 5

3. Slope intercept form of linear functions · We have learned that every linear function can be expressed by a function rule that looks like this : y = ___ x + ___

4. · In algebra, we call this form of function rule a slope intercept form. · You'll find it usually expressed as y = mx + b · y and x are variables. They vary! ·m and b are numbers, constant. They stay the same!

5. 40% of the 8th grade math EOG questions, are about finding the value of m or b using: ·The graph ·The function rule ·Coordinates of 2 points ·a real life situation So let's say it's a... VERY important lesson!

6. b a.k.a the y-intercept · For the real life situation, b is always the flat fee,the guaranteed salary... Basically the part of the cost (salary) that does not depend on the other variable ·On the graph, you can always read it where the line intersects the y-axis. Therefore it's called the y intercept!

7. y = mx + ..... y = mx + ...... Guided practice

9. Independent practice Find the y-intercept of each linear function

11. Vendredi 24 Septembre Warm up What is the y-intercept of the following lines?

12. What is the slope of a line? Slope : The number that determines the steepness of a line

13. Where do we see natural slopes???

16. Watch the 2nd video and try to take notes of the 4 different types of slope.

17. Slopes can be: · positive ·negative ·zero ·undefined *Look at the line from left to right (like reading)

20. cross country skiing

22. Is the slope positive, negative, undefined or none at all???

23. Is the slope positive, negative, undefined or none at all???

24. Is the slope positive, negative, undefined or none at all???

25. Is the slope positive, negative, undefined or none at all???

26. Is the slope positive, negative, undefined or none at all???

27. Is the slope positive, negative, undefined or none at all???

28. Is the slope positive, negative, undefined or none at all???

29. Is the slope positive, negative, undefined or none at all???

30. Is the slope positive, negative, undefined or none at all???

31. Review game

43. Lundi 27 Septembre Warm up 1) What is the y-intercept of this line? 2) Is the slope of this line positive, negative zero or undefined?

44. Quick review: What do we know so far on linear functions ?

45. Objective 1: Finding slope on the graph Watch the following segment of video (what is slope from 2:00 mark) and write down steps to find the slope of a line on the graph.

46. Finding slope on the graph step by step Step 1: Determine sign of the slope (+,-,...) Step 2: Pick 2 points on the line (corners of unit squares) Step 3: Draw a slope triangle Rise first, run second. Rise : up +, down - Run : right +, left - Step 4: Write the fraction rise/run, simplify, check the sign

47. Guided practice S tep 1: Step 2: Step 3: Step 4:

48. S tep 1: Step 2: Step 3: Step 4:

49. S tep 1: Step 2: Step 3: Step 4:

50. Independent practice: (will be evaluated) · Front: The 2 points are already picked for you (step 2), focus on the 3 other steps. ·Back page: You have to pick the 2 points, remember to pick them on corners of unit squares Chek with your partners, ask for help, do not stay passive. 90% of the learning happens here!

53. Mardi 28 Septembre Warm up

54. Homework check

57. Objective 2: Matching a linear equation with a graph Which linear equation describes the blue line? A . y = 3x + 2 B. y = -3x - 2 C. y = 3x - 2 D. y = 4x - 2 Step 1 : Find the y-intercept of the blue line. Eliminate answers based on the "b". St ep 2: Determine sign of slope. Eliminate answers based on the sign of "m" St ep 3: Find slope. You should have only one possible answer

58. Independent practice

60. Y = mx + b

61. Objective 2: Which linear equation describes the blue line? A. y = (2/3)x + 2 B. y = ( -3/2)x + 2 C. y = (3/2)x - 3 D. y = (-2/3)x + 2

62. Which graph corresponds to y = (1/2)x - 1 ?

63. Pop quiz 3

65. End of class game

68. Mercredi 29 Septembre Warm up y = 2x + 1?

69. Pop quiz 3 for the same 4 graphs, write the function rule

70. Homework check

71. Objective 3: Find the slope of a line knowing the coordinates of 2 points What is the slope of a line going through (1,2) and (3,6) ?

72. Could we do this without graphing?

73. Objective 3: Find the slope using coordinates of 2 points

74. Step by step guided practice Step 1: Mark (x 1 , y 1) and (x 2 , y 2) under the points. St ep 2: Write down the formula St ep 3: Plug in the numbers in your formula. Simplify

75. Find the slope of the line that goes through the two points given.

76. 1. 2. TRY: Find the slope of the line that goes through the two points given.

78. Jeudi 30 Septembre Warm up Find the slope of the line going through the following points

79. Homework check

80. Quiz 3 : study guide Obj 2: Match y=mx+b with graph

81. Objective 1 example problem S1: S2: S3: S4:

82. Objective 2: example problem Wh ich function rule best describes the blue line? A. y = 1x + 2 B. y = -2x + 1 C. y = 0.5x +1 D. y = 0.5x - 1 S1: S2: S3:

83. Objective 3 example problem Fi nd the slope of the line going through (-1,3) and ( 5, 1) S1: S2 S3:

84. Review game · Everyone in the group does the work! ·Rewards will go to the winners + the groups where I see REAL group work

90. Which line is best described by : y = -2x -1?

91. Which line best describes the function rule y = 1/2x + 1

93. Which function rule best describes the blue line? A. y = 4x - 1 B. y = 4x - 1 C. y = (-1/4)x + 1 D. y = (-1/4)x - 1

96. Vendredi 1er Octobre Warm up Wr ite the function rules that can describe the blue lines:

97. Quiz # 3 Ob jective 1: Find the slope of the following lines using the graph

99. Write the function rules that best describe the following lines: 6) 7) Obj. 2: Match a function rule with a graph

100. 8) Which function rule best describes the line? A. y = (1/2)x + 4 B. y = 4x + 2 C. y = -2x + 4 D. y = 2x + 4

101. 9) Which function rule best describes the line? A. y = -1x - 2 B. y = -3x - 2 C. y = 1x + 2 D. y = 1x - 2

102. 10) Which graph represents the function y = (-1/2)x + 3 ?

103. Find the slope of the lines going through: 11) (2,4) and (3,8) 12) (-1, 3) and (4, -7) 13) (-2,5) and (1,5) 14) (2,4) and (2,10) Obj. 3:

104. 15) Round √ 46 to the nearest tenth 16) Is √ 5 rational or irrational? 17) Is √ 49 rational or irrational? 18) Put √96 between 2 consecutive integers < √96 < 1 9) Is this a function? x y

105. 20.