2.4 using linear models
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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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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1) Modeling Real-World Data
x = independenty = dependent
(x, y) = (time, words typed )
(x1, y1) = (3, 174)
(x2, y2) = (6, 348)
(x3, y3) = (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 plane’s elevation as a function of the time it has been descending. Interpret the vertical intercept.
1) Modeling Real-World Data
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1) Modeling Real-World Data
Time (minutes)
(x, y) = (time, height)
(x1, y1) = (0, 8000)
(x2, y2) = (10, ?)
(x3, y3) = (20, ?)
10 20 30
6000
2000
4000
8000
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1) Modeling Real-World Data
Time (minutes)
Equation:
Remember… y = mx + b
10 20 30
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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2) Predicting with Linear Models
(x, y) = (months, subscribers)
(x1, y1) = (5, 5730)
(x2, y2) = (7, 6022)
(x3, y3) = (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)
(x1, y1) = (5, 5730)
(x2, y2) = (7, 6022)
(x3, y3) = (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)
(x1, y1) = (5, 5730)
(x2, y2) = (7, 6022)
(x3, y3) = (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)
(x1, y1) = (5, 5730)
(x2, y2) = (7, 6022)
(x3, y3) = (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
3 1 5 4 1 6
Grade (%)
65 35 90 74 45 87
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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 + b30
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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 + b30
Rise = 20
Run = 2
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Homework
p.81 #1-3, 8, 11, 12, 13, 19