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2.4 Using Linear Models. Modeling Real-World Data 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. 1) Modeling Real-World Data.
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2.4 Using Linear Models Modeling Real-World Data 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.
1) Modeling Real-World Data 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 ) (x1, y1) = (3, 174) (x2, y2) = (6, 348) (x3, y3) = (5, ?) Solution: 400 300 200 100 1 2 3 4 5 6 Time (minutes)
1) Modeling Real-World Data 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 plane’s elevation as a function of the time it has been descending. Interpret the vertical intercept.
1) Modeling Real-World Data (x, y) = (time, height) (x1, y1) = (0, 8000) (x2, y2) = (10, ?) (x3, y3) = (20, ?) 8000 6000 4000 2000 10 20 30 Time (minutes)
1) Modeling Real-World Data Equation: Remember… y = mx + b 8000 6000 4000 2000 10 20 30 Time (minutes)
2) Predicting with Linear Models • You can extrapolate with linear models to make predictions based on trends.
2) Predicting with Linear Models 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) (x1, y1) = (5, 5730) (x2, y2) = (7, 6022) (x3, y3) = (10, ?) Equation:y = mx + b 8000 6000 4000 2000 2 4 6 8 10 Time (months)
2) Predicting with Linear Models (x, y) = (months, subscribers) (x1, y1) = (5, 5730) (x2, y2) = (7, 6022) (x3, y3) = (10, ?) Equation:y = mx + b 8000 6000 4000 2000 2 4 6 8 10 Time (months)
2) Predicting with Linear Models (x, y) = (months, subscribers) (x1, y1) = (5, 5730) (x2, y2) = (7, 6022) (x3, y3) = (10, ?) Equation:y = mx + b 8000 6000 4000 2000 2 4 6 8 10 Time (months)
2) Predicting with Linear Models (x, y) = (months, subscribers) (x1, y1) = (5, 5730) (x2, y2) = (7, 6022) (x3, y3) = (10, 7000) Equation:y = mx + b 8000 rise = 1000 6000 run = 4 4000 y-intercept 2000 2 4 6 8 10 Time (months)
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. • Draw a scatter plot. Decide whether a linear model is reasonable. • Draw a trend line. Write the equation for the line.
Scatter Plots (x, y) = (hours studying, grade) (3, 65) (1, 35) (5, 90) (4, 74) (1, 45) (6, 87) Equation: y = mx + b 100 90 80 70 60 50 40 30 1 2 3 4 5 6 Hours studying
Scatter Plots • (x, y) = (hours studying, grade) • (3, 65) • (1, 35) • (5, 90) • (4, 74) • (1, 45) • (6, 87) • Based on the graph, is a linear model reasonable? 100 90 80 70 60 50 40 30 1 2 3 4 5 6 Hours studying
Scatter Plots (x, y) = (hours studying, grade) (3, 65) (1, 35) (5, 90) (4, 74) (1, 45) (6, 87) b) Equation: y = mx + b 100 90 80 70 60 Rise = 20 50 40 Run = 2 30 1 2 3 4 5 6 Hours studying
Homework p.81 #1-3, 8, 11, 12, 13, 19
