Line of Best Fit

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

Warm-Up Determine the correlation: Number of hours studying and test scores Number of hours watching TV and test scores Height and test scores Length of last name and test scores

Warm-Up Determine the correlation: Number of hours studying and test scores Number of hours watching TV and test scores Height and test scores Length of last name and test scores Positive Negative None None

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 -draw a line of best fit

EQ: How Do I Find the Line of Best Fit? 5/5/2019

Scatter Plot 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 scatterplot Note: All of the points are NOT connected

Slope Formula 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 Slope Intercept Form y = mx + b

Typing Speed (words/min) Example 1: The table shows Tammy’s speed at typing after a given number of weeks practicing. Create a scatterplot of the data and determine the line of best fit that represents the data trend. Practice Time (weeks) Typing Speed (words/min) 1 20 2 22 3 30 4 33 5 38 6 40

44 40 32 Typing Speed (wpm) 24 16 8 1 2 3 4 5 6 Practice Time (weeks)

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

Points: (2, 24) and (5, 36) 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 y = mx + b 24 = 4(2) + b 𝑚= 36−24 5−2 24 = 8 + b -8 -8 ______________ 𝑚= 12 3 16 = b 𝑚=4 y = 4x + 16

What does the slope mean in context? Each week of practice, Tammy’s typing speed increases by 4 words per minute What does the y-intercept mean in context? Before Tammy starts practice, she can 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 y = 4x + 16 y = 4(12) + 16 y = 48 + 16 y = 64 After 12 weeks of practice, Tammy will type 64 words per minute.

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

Guided Practice 1 The table shows the hours of TV watched weekly by 9 students and their test 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) 21 8 31 15 28 18 17 Math Test Score (%) 70 100 44 72 54 40 96 64

100 80 Math Quiz Score 60 40 20 6 12 18 24 30 36 Hours Watching TV

Guided Practice 1 What do the x and y variables represent? X: Hours spent watching TV Y: Math Quiz score

Guided Practice 1 Points: (6, 110) and (33, 30) 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 y = mx + b 30 = -2.96(30) + b 𝑚= 30−110 33−6 30 = -88.8 + b +88.8 _______________ +88.8 𝑚= −80 27 118.8 = b y = -2.96x + 118.8 𝑚=−2.96

Guided Practice 1 What does the slope mean in context? What does the y-intercept mean in context? For every hour of TV you watch, your quiz score decreases by -2.96%. Without watching any TV, you will score 118.8% on the quiz.

Guided Practice 1 Use your line of best fit to predict the quiz score of a student who watched 20 hours of TV y = -2.96x + 118.8 After watching TV for 20 hours, a student would score a 59.6% on their test. y = -2.96(20) + 118.8 y = -59.2 + 118.8 y = 59.6

Guided Practice 1 Use your line of best fit to predict the number of hours of TV watched if someone scored a 70% on their quiz. 70 = -2.96x + 118.8 If someone scored a 70 on their quiz, they watched 16.48 hours of TV -118.8 -118.8 ____________________ -48.8 = -2.96x _____ -2.96 _____ -2.96 16.48 = x