1
MA 15200
Lesson 24
Section 3.7
Certain formulas are called variation models.
These formulas show how one quantity
changes in relation to other quantities.
There are four types of variation:
Direct,
Inverse, Joint, and Combined.
All variation formulas (variation models) involve a
constant
k
.
I
Direct Variation.
13
S
h
=
This is a
direct variation
formula that says the salary of a person is 13 times
the hours worked.
The constant
k
is 13 ($13 is the hourly wage).
It is easy to understand,
that as the number of hours increases, so does the salary earned. The format for direct
variation is
y
kx
=
.
In
direct variation
(as long as the constant is positive) as
x
increases, so does
y
.
You can also see that this model would have a graph that is a line
with a positive slope of
k
and a
y
-intercept at 0.
Direct Variation:
If a situation is described by an equation in the form
y
kx
=
,
where
k
is a nonzero constant, we say that
y
varies directly as
x
or
y
is directly
proportional to
x
.
The number
k
is called the
constant of variation
or the
constant of
proportionality.
Steps for Solving a Direct Variation Problem:
1.
Write an equation that models the given English statement.
2.
Substitute the given values into the equation in step 1 and solve for
k
, the
constant.
3.

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