2­4 Using Linear Models
Objective:
Title: Jul 22­2:02 PM (1 of 13)
To write linear equations that model real world data
To make predictions from linear models
Check Skills You'll Need
Find the change in x and the change in y between each pair of points.
1) (­0.2, 9) and (3.4, 7.3)
2) (10, 17) and (11.5, 13.5)
Evaluate each function for the given values.
1
3) f(x) = x ­ 2 for x = ­3, 0, 2
4
3
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Modeling Real World Data
You can write linear equations to model real­world problems.
Example: Transportation
Jacksonville, Florida has an elevation of 12 ft. above sea level. A hot­air balloon taking off from Jacksonville rises 50 ft/min. Write an equation to model the balloon's elevation as a function of time. Graph the equation. Interpret the intercept at which the graph intersects the vertical axis. Title: Jul 22­2:02 PM (3 of 13)
Jacksonville, Florida has an elevation of 12 ft. above sea level. A hot­air balloon taking off from Jacksonville rises 50 ft/min. Write an equation to model the balloon's elevation as a function of time. Graph the equation. Interpret the intercept at which the graph intersects the vertical axis. Relate:
balloon's elevation = (rate)(time) + starting elevation
Define:
Let h = the balloon's elevation
Let t = time (in minutes) since the hot­air balloon lifted off
Write:
h = (50)(t) + 12
h = 50t + 12
h
The h­intercept is (0, 12).
The t­coordinate, 0, represents the time at the start of the trip.
30
The h­coordinate, 12, represents the elevation of the balloon at the start of the trip.
.
20
10 (0, 12)
2
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4
6
t
A spring has a length of 8 cm when a 20­g mass hangs at the bottom end. Each additional gram stretches the spring another 0.15 cm. Write an equation to model the length y of the spring as a function of the mass x of the attached weight.
Step 1:
Identify the data points (20, 8) and (21, 8.15) as (x 1, y1) and (x2, y2).
Step 2:
Find the slope of the line.
Step 3:
Use one of the points and the point­slope form to
write an equation for the line.
y = 0.15x + 5
Answer
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Using the previous equation, what mass could be needed to stretch the spring to a length of 9.5 cm?
y = 0.15x + 5
9.5 = 0.15x + 5
4.5 = 0.15x
30 = x
Title: Jul 22­2:02 PM (6 of 13)
A scatter plot is a graph that relates two different sets of data by plotting the data as ordered pairs. Strong,
negative
No
A trend line is a line that approximates the relationship between the data sets of a scatter plot. You can use a trend line to make predictions.
Title: Jul 22­2:02 PM (7 of 13)
A woman is considering buying a 1999 car. She researches prices for various years of the same model car and records the data in a table.
Model Year
Prices
2000
2001
$5784 $6810
2002
$8237
2003
$9660
2004
$10,948
$5435
$7751
$9127
$10,455
j
$6207
Let x represent model year (in years since 1999)
Let y represent the price of the car
Draw a scatter plot
Title: Aug 10­10:16 AM (8 of 13)
Model Year
Prices
2000
2001
$5784 $6810
2002
$8237
2003
$9660
2004
$10,948
$5435
$7751
$9127
$10,455
j
$6207
8
6
4
2
2
4
6
years (since 1999)
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8
Model Year
Prices
2000
2001
$5784 $6810
2002
$8237
2003
$9660
2004
$10,948
$5435
$7751
$9127
$10,455
j
$6207
8
6
Draw a trend line
4
2
2
4
6
years (since 1999)
Title: Aug 10­10:16 AM (10 of 13)
8
Model Year
Prices
2000
2001
$5784 $6810
2002
$8237
2003
$9660
2004
$10,948
$5435
$7751
$9127
$10,455
j
$6207
8
Write the equation of the line
6
4
2
2
4
6
years (since 1999)
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8
If the car's asking price is $4,200, is this price reasonable?
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Homework
Homework
Pages 81 ­ 84
#'s: 1 ­ 14, 20, 21, 35 ­ 45
2.1 ­ 2.3 Quiz tomorrow!!!!
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