Linear Scatter Plots SID 6 SID 7 SID

Linear Scatter Plots S-ID. 6, S-ID. 7, S-ID. 8

Table of Contents 58: Guided Practice (in Workbook) 59: How Do I Find a Line of Best Fit?

EQ: How Do I Find the Line of 10/22/2021 Best Fit?

Scatter Plot Shows a set of related data using points on a graph Line of A line which best represents Best Fit the data on a scatterplot

X-Axis Independent variable Normally the first row/column in a table It’s the constant term: temperature, time, etc

Y-Axis Dependent variable Normally the second row or column in a table It’s the changing term: height, money, etc

Example 1: The table represents the relationship between the number of minutes a basketball player plays in a game and the number of points scored. Plot and approximate the line of best fit Time 2 8 12 18 25 30 35 (min) Pts 3 6 9 13 16 20 24 24 P 20 o 16 i n 12 t 8 s 4 6 12 18 24 Time (min) 30

(18, 12) (33, 22) = 22 – 12 33 – 18 = 10 15 = 0. 67

Pt: (18, 12) M: 0. 67 y – y 1 = m(x – x 1) y – 12 = 0. 67(x – 18) y – 12 = 0. 67 x – 12. 06 +12 _________ y = 0. 67 x – 0. 06

If 50 minutes has been played, about how many points would be scored? y = 0. 67 x – 0. 06 y = 0. 67(50) – 0. 06 y = 33. 5 – 0. 06 y = 33. 44 After 50 minutes of play, about 33 points would be scored.

If 62 points had been scored, how many minutes was played in the game? y = 0. 67 x – 0. 06 62 = 0. 67 x – 0. 06 + 0. 06 _________ + 0. 06 62. 06 ____ = 0. 67 x ____ 0. 67 92. 62 = x If 62 points have been scored, then 93 mins has been played

Typing Speed (wpm) Guided Practice One (Page 9) 40 32 24 16 8 8 2 4 6 Practice Time (weeks)

Guided Practice One (Page 9) Cont Provide the symbolic representation: (1, 20) and (3, 28) m = 28 – 20 3– 1 m=8 2 m=4 y = mx + b 20 = 4(1) + b 20 = 4 + b -4 -4 _______ 16 = b y = 4 x + 16

Guided Practice One (Page 9) Cont What does the slope and y-intercept mean in context? Slope: Each week Tammy types, she increases her typing by 4 words a minute Y-Intercept: Before any practice, Tammy can type 16 words a minute

Guided Practice One (Page 9) Cont Predict how many words per minute Tammy will type after 12 weeks y = 4 x + 16 y = 4(12) + 16 y = 48 + 16 y = 64 She will be able to type 64 words per minute

Guided Practice One (Page 9) Cont How many weeks of practice will it take for Tammy to type 100 words per minute? It will take Tammy y = 4 x + 16 21 weeks to type 100 = 4 x + 16 100 words per minute -16 _______ 84 4 x __ =___ 4 4 21 = y

Math Quiz Score (%) Guided Practice Two (Page 11) 100 80 60 40 20 6 12 TV (hours) 18 24 30

Guided Practice Two (Page 10) Cont Provide the symbolic representation: (9, 100) and (30, 40) m = 40 - 100 30 - 9 m = -60 21 m = -2. 88 y – y 1 = m(x – x 1) y – 100 = -2. 88(x – 9) y – 100 = -2. 88 x + 23. 06 +100 __________ y = -2. 88 x + 123. 06

Guided Practice Two (Page 10) Cont What does the slope and y-intercept mean in context? Slope: For every hour of TV watched, your score decreases -2. 88% Y-Intercept: If no TV was watched, you would have 123%

Guided Practice Two (Page 10) Cont Predict the quiz score of a student who watched 20 hours of TV You would y = -2. 88 + 123. 06 score a y = -2. 88(20) + 123. 06 65. 4% on the quiz y = -57. 6 + 123. 06 y = 65. 4%

Guided Practice Two (Page 10) Cont Predict the number of hours of TV watched if a student scored a 70 on their quiz. You would y = -2. 88 x + 123. 06 have 70 = -2. 88 x + 123. 06 watched -123. 06 _________ TV for -53. 06 -2. 88 x _____ = _____ about 19 -2. 88 hours 19 = y

Questions What is important to remember about picking points on your line? Why do you think the slope is in decimal form and not a fraction? What is a real life example of positive correlation? What is a real life example of negative correlation?

Homework today is: Page 13 – 15 in your workbook. Make sure to rip it out and staple it before turning it in. Answers will be up shortly

CW/HW Answers Page 13 Page 15 a. y = 1. 875 x – 50 c. About 40 tons d. About 5. 33 feet a. y = 0. 57 x – 1044. 3 c. About 95. 7 years d. About 1902 Page 14 a. y = -27. 78 x + 600 c. About 377. 76 acres d. -316. 74 acres