Lesson 4.6 Best Fit Line
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1 Lesson 4.6 Best Fit Line Concept: Using & Interpreting Best Fit Lines EQs: -How do we determine a line of best fit from a scatter plot? (S.ID.6 a,c) -What does the slope and intercept tell me about the data? (S.ID.7) Vocabulary: Scatter Plot, Slope, Intercept, Line of best fit : Fitting Linear Functions to Data
2 Dear Teacher On a sheet of paper, write to your teacher what you know about best fit lines and what you hope to learn after today s lesson : Fitting Linear Functions to Data 2
3 Before you can find the line of Graph your data best fit.. Determine if the data can be represented using a linear model does the data look linear??? Draw a line through the data that is close to most points. Some values should be above the line and some values should be below the line. Now you can write the equation of the line. Let s try one together : Fitting Linear Functions to Data 3
4 Pablo s science class is growing plants. He recorded the height of his plant each day for 10 days. The plant s height, in cm, over time is in the scatter plot : Fitting Linear Functions to Data
5 GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (7, 14), (8, 16) 4.2.4: Fitting Linear Functions to Data 5
6 GO Best Fit Line Steps 1. Identify two points on the line of best fit 2. Find the slope of the line using the points Example (7, 14), (8, 16) m = = 2 1 = : Fitting Linear Functions to Data 6
7 GO Best Fit Line Steps 1. Identify two points on the line of best fit 2. Find the slope of the line using the points 3. Substitute into Example (7, 14), (8, 16) m = = 2 1 = 2 y = 2(x 7) + 14 y = m(x x 1 ) + y : Fitting Linear Functions to Data 7
8 GO Best Fit Line Steps 1. Identify two points on the line of best fit 2. Find the slope of the line using the points 3. Substitute into Example (7, 14), (8, 16) m = = 2 1 = 2 y = 2(x 7) + 14 y = m(x x 1 ) + y 1 4. Simplify y = 2x y = 2x 4.2.4: Fitting Linear Functions to Data 8
9 (Write this below your GO) Interpret the slope and y-intercept y = 2x Slope value: Slope units: Y-intercept value: Y-intercept unit: Interpretation: : Fitting Linear Functions to Data
10 Guided Practice Example 1 A weather team records the weather each hour after sunrise one morning in May. The hours after sunrise and the temperature in degrees Fahrenheit are in the table to the right. Can the temperature 0 7 hours after sunrise be represented by a linear function? If yes, find the equation of the function. Graph the points!!! Hours after sunrise Temperature in F : Fitting Linear Functions to Data
11 Temperature ( F) Guided Practice: Example 1, continued 1. Create a scatter plot of the data. Let the x-axis represent hours after sunrise and the y-axis represent the temperature in degrees Fahrenheit. Hours after sunrise : Fitting Linear Functions to Data
12 Guided Practice: Example 1, continued 2. Determine if the data can be represented by a linear function. The graph of a linear equation is a line. If the data looks like it could fit a line, then a linear equation could be used to represent the data. The temperatures appear to increase in a line, and a linear equation could be used to represent the data set : Fitting Linear Functions to Data
13 Guided Practice: Example 1, continued 3. Draw a line to estimate the data set. Two points in the data set can be used to draw a line that estimates that data. When the line is drawn, some of the data values should be above the line, and some should be below the line. A line through (2, 56) and (6, 64) looks like a good fit for the data : Fitting Linear Functions to Data
14 Temperature ( F) Guided Practice: Example 1, continued Hours after sunrise : Fitting Linear Functions to Data
15 GO Best Fit Line Steps Example
16 GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (2, 56), (6, 64) : Fitting Linear Functions to Data 16
17 GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (2, 56), (6, 64) 2. Find the slope of the line using the points m = = 8 4 = : Fitting Linear Functions to Data 17
18 GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (2, 56), (6, 64) 2. Find the slope of the line using the points m = = 8 4 = 2 3. Substitute into y = 2(x 2) + 56 y = m(x x 1 ) + y : Fitting Linear Functions to Data 18
19 GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (2, 56), (6, 64) 2. Find the slope of the line using the points m = = 8 4 = 2 3. Substitute into y = 2(x 2) + 56 y = m(x x 1 ) + y 1 4. Simplify y = 2x y = 2x : Fitting Linear Functions to Data 19
20 Interpret the slope and y-intercept y = 2x + 52 Slope value: Slope units: Y-intercept value: Y-intercept unit: Interpretation: : Fitting Linear Functions to Data
21 Guided Practice - Example 2 Can the speed between 0 and 8 seconds be represented by a linear function? If yes, find the equation of the function : Fitting Linear Functions to Data
22 Guided Practice: Example 2, continued 1. Create a scatter plot of the data. Let the x-axis represent time and the y-axis represent speed : Fitting Linear Functions to Data
23 Guided Practice: Example 2, continued 2. Determine if the data can be represented by a linear function : Fitting Linear Functions to Data
24 Guided Practice - Example 3 Automated tractors can mow lawns without being driven by a person. A company runs trials using fields of different sizes, and records the amount of time it takes the tractor to mow each field. The field sizes are measured in acres. Can the time to mow acres of a field be represented by a linear function? If yes, find the equation of the function. Acres Time in hours : Fitting Linear Functions to Data
25 Time Guided Practice: Example 3, continued 1. Create a scatter plot of the data. Let the x-axis represent the acres and the y-axis represent the time in hours. Acres : Fitting Linear Functions to Data
26 Guided Practice: Example 3, continued 2. Determine if the data can be represented by a linear function. The graph of a linear equation is a line. If the data looks like it could fit a line, then a linear equation could be used to represent the data. The time appears to increase in a line, and a linear equation could be used to represent the data set : Fitting Linear Functions to Data
27 Guided Practice: Example 3, continued 3. Draw a line to estimate the data set. Two points in the data set can be used to draw a line that estimates the data. When the line is drawn, some of the data values should be above the line, and some should be below the line. A line through (7, 10) and (40, 112) looks like a good fit for the data : Fitting Linear Functions to Data
28 Time Guided Practice: Example 3, continued Acres : Fitting Linear Functions to Data
29 GO Best Fit Line Steps Example
30 GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (7, 10) and (40, 112) : Fitting Linear Functions to Data 30
31 GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (7, 10) and (40, 112) 2. Find the slope of the line using the points m = = = : Fitting Linear Functions to Data 31
32 GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (7, 10) and (40, 112) 2. Find the slope of the line using the points m = = = Substitute into y = 3.09(x 7) + 10 y = m(x x 1 ) + y : Fitting Linear Functions to Data 32
33 GO Best Fit Line Steps 1. Identify two points on the line of best fit Example (7, 10) and (40, 112) 2. Find the slope of the line using the points m = = = Substitute into y = 3.09(x 7) + 10 y = m(x x 1 ) + y 1 4. Simplify y = 3.09x y = 3.09x : Fitting Linear Functions to Data 33
34 Interpret the slope and y-intercept y = 3.09x Slope value: Slope units: Y-intercept value: Y-intercept unit: Interpretation: : Fitting Linear Functions to Data
35 Resource 35
36 The Important Thing On a sheet of paper, write down three things you learned today. Out of those three, write which one is most important and why. 36
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