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2.4 Using Linear Models 1.Modeling Real-World Data 2.Predicting with Linear Models

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1) Modeling Real-World Data Big idea… Use linear equations to create graphs of real-world situations. Then use these graphs to make predictions about past and future trends.

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Example 1: There were 174 words typed in 3 minutes. There were 348 words typed in 6 minutes. How many words were typed in 5 minutes? 1) Modeling Real-World Data

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x = independent y = dependent (x, y) = (time, words typed ) (x 1, y 1 ) = (3, 174) (x 2, y 2 ) = (6, 348) (x 3, y 3 ) = (5, ?) Solution: Time (minutes) 1 2 3 4 5 6 100 200 300 400

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Example 2: Suppose an airplane descends at a rate of 300 ft/min from an elevation of 8000ft. Draw a graph and write an equation to model the planes elevation as a function of the time it has been descending. Interpret the vertical intercept. 1) Modeling Real-World Data

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Time (minutes) (x, y) = (time, height) (x 1, y 1 ) = (0, 8000) (x 2, y 2 ) = (10, ?) (x 3, y 3 ) = (20, ?) 102030 6000 2000 4000 8000

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1) Modeling Real-World Data Time (minutes) Equation: Remember… y = mx + b 102030 6000 2000 4000 8000

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2) Predicting with Linear Models You can extrapolate with linear models to make predictions based on trends.

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Example 1: After 5 months the number of subscribers to a newspaper was 5730. After 7 months the number of subscribers was 6022. Write an equation for the function. How many subscribers will there be after 10 months? 2) Predicting with Linear Models

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(x, y) = (months, subscribers) (x 1, y 1 ) = (5, 5730) (x 2, y 2 ) = (7, 6022) (x 3, y 3 ) = (10, ?) Equation: y = mx + b Time (months) 2 4 6 8 10 2000 4000 6000 8000

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2) Predicting with Linear Models (x, y) = (months, subscribers) (x 1, y 1 ) = (5, 5730) (x 2, y 2 ) = (7, 6022) (x 3, y 3 ) = (10, ?) Equation: y = mx + b Time (months) 2 4 6 8 10 2000 4000 6000 8000

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2) Predicting with Linear Models (x, y) = (months, subscribers) (x 1, y 1 ) = (5, 5730) (x 2, y 2 ) = (7, 6022) (x 3, y 3 ) = (10, ?) Equation: y = mx + b Time (months) 2 4 6 8 10 2000 4000 6000 8000

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2) Predicting with Linear Models (x, y) = (months, subscribers) (x 1, y 1 ) = (5, 5730) (x 2, y 2 ) = (7, 6022) (x 3, y 3 ) = (10, 7000) Equation: y = mx + b Time (months) 2 4 6 8 10 2000 4000 6000 8000 y-intercept run = 4 rise = 1000

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Scatter Plots Connect the dots with a trend line to see if there is a trend in the data

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Types of Scatter Plots Strong, positive correlation Weak, positive correlation

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Types of Scatter Plots Strong, negative correlation Weak, negative correlation

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Types of Scatter Plots No correlation

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Scatter Plots Example 1: The data table below shows the relationship between hours spent studying and student grade. a)Draw a scatter plot. Decide whether a linear model is reasonable. b)Draw a trend line. Write the equation for the line. Hours studying 315416 Grade (%) 653590744587

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Scatter Plots Hours studying 1 2 3 4 5 6 40 50 70 60 90 80 100 (x, y) = (hours studying, grade) (3, 65) (1, 35) (5, 90) (4, 74) (1, 45) (6, 87) Equation: y = mx + b 30

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Scatter Plots Hours studying 1 2 3 4 5 6 40 50 70 60 90 80 100 (x, y) = (hours studying, grade) (3, 65) (1, 35) (5, 90) (4, 74) (1, 45) (6, 87) a)Based on the graph, is a linear model reasonable? 30

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Scatter Plots Hours studying 1 2 3 4 5 6 40 50 70 60 90 80 100 (x, y) = (hours studying, grade) (3, 65) (1, 35) (5, 90) (4, 74) (1, 45) (6, 87) b) Equation: y = mx + b 30 Rise = 20 Run = 2

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Assignment p.81 #1-3, 8, 11, 12, 13, 19,

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2.4 Using Linear Models. The Trick: Converting Word Problems into Equations Warm Up: –How many ways can a $50 bill be changed into $5 and $20 bills. Work.

2.4 Using Linear Models. The Trick: Converting Word Problems into Equations Warm Up: –How many ways can a $50 bill be changed into $5 and $20 bills. Work.

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