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

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

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.

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

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

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

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

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

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

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

(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

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

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

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

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

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

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

Types of Scatter Plots No correlation

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

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

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

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

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

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