Warm up 1. Calculate the slope of a line passing through (2, 3) and (1, 5). 2. Write the equation of a line given a slope of 3 and a y-intercept of 4 (hint: use y = mx + b). 3. Calculate the slope of a line given the table of values below: 4.2.4: Fitting Linear Functions to Data1 x1357 y

Unit 4 Part B Concept: Best fit Line EQ: How do we create a line of best fit to represent data? Vocabulary: R – correlation coefficient y = mx + b slope 4.2.4: Fitting Linear Functions to Data2

Standard… S.ID.6cFit a linear function for a scatter plot that suggests a linear association : Fitting Linear Functions to Data3

Before you can find the line of best fit….. Graph your data 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 will be below the line. Now you can write the equation of the line. Let’s try one together : Fitting Linear Functions to Data4

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 : Fitting Linear Functions to Data Hours after sunrise Temperature in ˚F Graph the points!!!

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 : Fitting Linear Functions to Data Temperature (°F) Hours after sunrise

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

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

Guided Practice: Example 1, continued : Fitting Linear Functions to Data Temperature (°F) Hours after sunrise

GO Best Fit Line Steps Example

GO Best Fit Line Steps 1.Identify two points on the line of best fit Example (2, 56), (6, 64) 4.2.4: Fitting Linear Functions to Data11

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 (2, 56), (6, 64) 4.2.4: Fitting Linear Functions to Data12

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 y = m(x – x 1 ) + y 1 4. Example (2, 56), (6, 64) 4.2.4: Fitting Linear Functions to Data13 y = 2(x – 2) + 56

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 y = m(x – x 1 ) + y 1 4. Simplify Example (2, 56), (6, 64) 4.2.4: Fitting Linear Functions to Data14 y = 2(x – 2) + 56 y = 2x – y = 2x +52

Guided Practice Example 2 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 : Fitting Linear Functions to Data Acres Time in hours

Guided Practice: Example 2, continued Can the time to mow acres of a field be represented by a linear function? If yes, find the equation of the function : Fitting Linear Functions to Data

Guided Practice: Example 2, 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 : Fitting Linear Functions to Data Time Acres

Guided Practice: Example 2, 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

Guided Practice: Example 2, 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

Guided Practice: Example 2, continued : Fitting Linear Functions to Data Time Acres

GO Best Fit Line Steps Example

GO Best Fit Line Steps 1.Identify two points on the line of best fit Example (7, 10) and (40, 112) 4.2.4: Fitting Linear Functions to Data22

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, 10) and (40, 112) 4.2.4: Fitting Linear Functions to Data23

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 y = m(x – x 1 ) + y 1 4. Example (7, 10) and (40, 112) 4.2.4: Fitting Linear Functions to Data24 y = 3.09(x – 7) + 10

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 y = m(x – x 1 ) + y 1 4. Simplify Example (7, 10) and (40, 112) 4.2.4: Fitting Linear Functions to Data25 y = 3.09(x – 7) + 10 y = 3.09x – y = 3.09x – 11.63

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