Math Learning Center
Boise State
©2010
Linear Modeling
Business
Mathematical Modeling is simply the act of building a model (usually in the form of graphs) which
provides a “picture” of a situation that is based in a numerical situation.
Linear Modeling is Mathematical Modeling where the graph is a line, hence linear.
Linear Modeling
occurs any time the rate of change is constant.
Let’s build two examples.
Example 1:
An auto manufacturer has a factory which is open 24 hours a day and produces 10 finished cars per
hour.
This model has a constant rate of change in that each hour 10 additional cars are produced.
Hence we will want to build a linear model.
To begin to build our linear model, let’s pick two points
How many cars will be built in an hour?
______
Enter the answer in point form:
(
,
)
(Answer in point form:
(
1
,
10
))
How many cars will be built in 24 hours?
______
Enter the answer in point form:
(
,
)
Now that we have two points, let’s create a graph. Wait, before we begin to graph, we must first choose
letters to represent our variables.
Since, we currently are in a math course, it would be easy to choose
x
and
y
as our representative letters.
But what do
x
and
y
mean?
Using the letters, x and y, in math
makes perfect sense as we are able to move from one mathematical concept to the next with a strong
level of consistency and thus, math is easier to learn from chapter to
chapter and course to course.
When we leave math and move to other subjects, such as business,
we will choose letters which reflect the situation we are modeling.
In
this case, let’s use
t
to represent time in hours and
n
to represent the
number of auto’s completed.
In this case, a general point will be in
the form (
t ,
n
).
The variable
t
, representing time, is called the independent variable
and will be placed on the horizontal axis when graphing.
The variable
n
, representing number of autos completed, is called the
dependent variable (this is because the number of autos completed
depends on the time allowed).
The vertical axis will be used to
represent
n
.
Side note:
Many students have
difficulty when we use letters
other than x and y.
When
students enroll in other courses
which use mathematical
modeling and do not use x and y
as the variable, they often have
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 Fall '09
 ALINASCHIMPF
 Math, Algebra, Derivative, Math Learning Center

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