Transcript Direct Variation

Direct Variation
Talking about the relationship
between variables in a new way!!!
Fun, Huh?
Many relationships in every day life involve a
relationship between measurable quantities
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Your pay is related directly to the hours you work, given a fixed
hourly wage
The distance you travel is related directly to the hours you
drive, given a fixed rate of speed
The number of words typed is related directly to the time spent
typing, given a fixed number of words per minute.
The amount of money that a magazine pays for an article is
related directly to the number of words, given a fixed amount of
money paid per word
The volume of a dry gas is related directly to its temperature,
given a fixed pressure
There are many ways to say the same
thing
y is related directly to x
 x and y vary directly
 y varies directly as x
 y is directly proportional to x
 y is dependent on x
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Constant of variation
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.
Note that in each of the preceding examples
the GIVEN is constant
This is called the constant of variation
The variable k is assigned to this constant
The equation y = kx is the mathematical way
to say the y is related directly to x
Sample problem
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The variables x and y vary directly . When
x = - 3 and y = -30.
Write an equation that relates x and y
Find the value of y when x = 8
Solution
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Recall y = kx. Now substitute numbers in for
what you know.
-30 = k (-3)
10 = k
Using that information you can write the
equation that relates x and y: y = 10x
Now we can solve that equation when
x=8
y = 10 x
y = 10(8)
y= 80
Problems of direct variation can also
be solved using proportions
y1 y2

x1 x2
Sample
30 y2

3 8
One more problem
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The forearm lengths and body
heights in inches of five people
are shown in the table.
Write a direct variation model
that relates body length B to
forearm length F
B = 7.5 F
Estimate the body length of a
person whose forearm length is
10 inches
75 in
F
7.0
7.5
8.0
8.5
9.0
B
52.5
55.5
58.4
63.5
68.4