# 5 5 Modeling with Linear Equations Goal Write and use a linear equation to solve a real life problem Key Words •linear model •rate of change E

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```					5.5   Modeling with Linear Equations

Goal
Write and use a linear equation to
solve a real-life problem.
Key Words
•linear model
•rate of change
EXAMPLE   1   Write a Linear Model

From 1985 through 1997, the number of movie
theaters in the United States increased by 750
per year. In 1993, there were about 26,000
theaters. Write a linear model for the number
of theaters y. Let t = 0 represent 1985.
Checkpoint        Write a Linear Model

1. From 1985 through 1997, movie attendance in the United
States increased by about 25 million per year. In 1994,
movie attendance was about 1300 million. Write a linear
model for movie attendance y (in millions). Let t = 0
represent 1985.
EXAMPLE      2       Use a Linear Model to Predict

Use the linear model y = 750t + 20,000 to predict
the number of theaters in the year 2005. Recall
that t = 0 represents the year 1985.
Algebraic Approach
EXAMPLE        2    Use a Linear Model to Predict

Use the linear model y = 750t + 20,000 to predict
the number of theaters in the year 2005. Recall
that t = 0 represents the year 1985.
Graphical Approach        U.S. Movie Theaters

40,000
Number of theaters

30,000

20,000

0
0     4        8     12     16        20   24   28
Years since 1985
Checkpoint         Use a Linear Model to Predict

Use the linear model you wrote for Checkpoint 1 to predict
the movie attendance in the year 2005. Let t = 0 represent the
year 1985.
Algebraic Approach
Checkpoint           Use a Linear Model to Predict

Use the linear model you wrote for Checkpoint 1 to predict
the movie attendance in the year 2005. Let t = 0 represent the
year 1985.
Graphical Approach
Example 1 From 1986 to 1999, a toy
company had an increase in the sales of one
of its stuffed animals by 900 per year. In
1996, the company sold 17,000 of the stuffed
animals. Write a linear model for the
number of stuffed animals sold y. Let t = 0
represent the year 1986.
Example 2 Use the linear model in the
previous example to predict the number of
stuffed animals sold in the year 2004. Recall
that t = 0 represents the year 1986.
y = 900 t + 8000
Homework
pp. 301 #6-17, 24-32,
35, 36
EXAMPLE      1       Write a Linear Model
5.5       Modeling with Linear Equations
From 1985 through 1997, the number of movie
theaters in the United States increased by 750
per year. In 1993, there were about 26,000
Goal                                               theaters. Write a linear model for the number
Write and use a linear equation to                 of theaters y. Let t = 0 represent 1985.
solve a real-life problem.
Key Words
•linear model
•rate of change

Checkpoint                           Write a Linear Model                      EXAMPLE      2       Use a Linear Model to Predict

1. From 1985 through 1997, movie attendance in the United                          Use the linear model y = 750t + 20,000 to predict
States increased by about 25 million per year. In 1994,                         the number of theaters in the year 2005. Recall
movie attendance was about 1300 million. Write a linear                         that t = 0 represents the year 1985.
model for movie attendance y (in millions). Let t = 0
Algebraic Approach
represent 1985.

EXAMPLE          2    Use a Linear Model to Predict          Checkpoint         Use a Linear Model to Predict

Use the linear model y = 750t + 20,000 to predict                    Use the linear model you wrote for Checkpoint 1 to predict
the number of theaters in the year 2005. Recall                      the movie attendance in the year 2005. Let t = 0 represent the
that t = 0 represents the year 1985.                                 year 1985.
Graphical Approach          U.S. Movie Theaters
Algebraic Approach

40,000

30,000

20,000
Number of theaters

0
0       4        8     12     16        20   24   28
Years since 1985
Checkpoint           Use a Linear Model to Predict              Example 1 From 1986 to 1999, a toy
Use the linear model you wrote for Checkpoint 1 to predict       company had an increase in the sales of one
the movie attendance in the year 2005. Let t = 0 represent the   of its stuffed animals by 900 per year. In
year 1985.                                                       1996, the company sold 17,000 of the stuffed
Graphical Approach                                              animals. Write a linear model for the
number of stuffed animals sold y. Let t = 0
represent the year 1986.

Example 2 Use the linear model in the
previous example to predict the number of
stuffed animals sold in the year 2004.
Recall that t = 0 represents the year 1986.
y = 900 t + 8000                                                              Homework
pp. 301 #6-17, 24-32,
35, 36

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