2.4 Using Linear Models
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2.4 Using Linear Models 1. Modeling Real-World Data 2. Predicting with 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 Presentation
Transcript of 2.4 Using Linear Models
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
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
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
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
1) Modeling Real-World Data
Time (minutes)
Equation:
Remember… y = mx + b
10 20 30
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
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
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
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
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
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
3 1 5 4 1 6
Grade (%)
65 35 90 74 45 87
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
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?
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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
Homework
p.81 #1-3, 8, 11, 12, 13, 19
