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

Table of Contents 45: How Do I Find the Line of Best Fit? 44: Warm-Up, Guided Practice

Warm-Up Determine the correlation a) Number of hours studying and test scores b) Number of hours watching TV and test scores c) Height and test score Positive Negative None

Warm-Up Find the equation of the line for the following graphs:

Learning Intention/Success Criteria LI: We are learning to find the line of best fit. SC: I know how to -graph data points -find the slope between two points -find the y-intercept with two points

EQ: How Do I Find the Line of Best Fit? 1/11/2019

Scatter Plot Line of Best Fit A graph of related data, where the data values are plotted (x, y) Line of Best Fit A line used to model the data on a scatter plot **All of the points do not need to be connected**

Slope Formula m = y2 – y1 x2 – x1 Slope Intercept Form y = mx + b

Typing Speed (Words per Minute) Example 1: The table shows Tammy’s speed at typing after a given number of weeks practicing. Create a scatter plot of the data and determine the line of best fit that represents the data trend. Practice time (weeks) Typing Speed (Words per Minute) 1 20 2 22 3 30 4 33 5 38 6 40 7 44

40 32 Typing Speed (wpm) 24 16 8 1 2 3 4 5 6 7 Practice Time (Weeks)

(1, 20) and (6, 40) m = y2 – y1 x2 – x1 y = mx + b 20 = 4(1) + b m = 40 – 20 6 - 1 20 = 4 + b -4 -4 ________________ m = 20 5 16 = b m = 4 y = 4x + 16

What do the x and y variables represent? The amount of weeks practicing X: Y: Tammy’s typing speed

What does the slope mean in context? Each week of practice, Tammy can type 4 more words per minute What does the y-intercept mean in context? Before practice typing, Tammy could type 16 words per minute

Use your line of best fit to predict how many words per minute Tammy will type after 12 weeks of practice. After 12 weeks of practice, Tammy will type 64 words per minute. y = 4x + 16 y = 4(12) + 16 y = 48 + 16 y = 64

Use your line of best fit to predict how many weeks of practice it will take for Tammy to type 100 words per minute. In order for Tammy to type 100 words per minute, she needs to practice for 21 weeks. y = 4x + 16 100 = 4x + 16 -16 -16 ________________ 84 = 4x __ 4 __ 4 21 = x

Guided Practice 1 The table shows the hours of TV watched weekly by 9 students and their scores on a math test. Create a scatter plot of the data and determine the line of best fit that represents the data trend. TV Watched (hours) Math Test Score (%) 21 70 8 100 31 44 15 72 54 28 40 10 20 18 96 17 64

100 80 Math Quiz Score (%) 60 40 20 6 12 18 24 30 Hours Watching TV

(21, 70) and (30, 40) m = y2 – y1 x2 – x1 y = mx + b 40 = -3.33(30) + b m = 40 – 70 30 - 21 40 = -99.9 + b +99.9 +99.9 ____________________ m = -30 9 139.9 = b m = -3.33 y = -3.33x + 139.9

What do the x and y variables represent? X: Y: The amount of hours of TV watched The score on a test What does the slope mean in context? For every hour to TV watched, your test score decreases by 3.33 percent.

What does the y-intercept mean in context? Without watching any TV, you will score 139.9% on the quiz.

Use your line of best fit to predict the quiz score of a student who watched 20 hours of TV y = -3.33x + 139.9 y = -3.33(20) + 139.9 y = -66.6 + 139.9 After watching 20 hours of TV, a student should score a 73.3% on the test y = 73.3

Use your line of best fit to predict the number of TV someone watched if they scored a 70 on the quiz If someone scored a 70 on their quiz, they watched 20.99 hours to TV y = -3.33x + 139.9 70 = -3.33x + 139.9 -139.9 -139.9 _____________________ -69.9 = -3.33x _____ -3.33 _____ -3.33 20.99 = x

Homework For the rest of class, please work on your homework. Check your answers on the class website: Masikalgebra.weebly.com