Math Learning Center
Boise State
©2010
Linear Modeling
STEM
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 on 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:
In physics, momentum is linearly associated with
velocity of an object.
Hence, we will want to build a
linear model.
To begin to build our linear model, let’s
pick two points.
For the first point when an auto is traveling 5 meters per
second (about 11 miles per hour), the momentum of the
auto is 7500 kg m/s.
(Note:
kg m/s is just shorthand for
the units of measurement of momentum which is kilograms times meters divided by seconds.)
Enter the answer in coordinate form:
(
,
)
(Answer in coordinate form: (
5 ,
7500
))
For the second point, when the auto is traveling 25 meters per second, the momentum is 37,500 kg m/s.
Enter the answer in coordinate 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 physics, we
will choose our letters which reflect the situation we are modeling.
In
this case, physicists use
g
to represent velocity and
G
to represent the
momentum.
In this case, a general point will be in the form (
gu G
).
The variable