PATTERNS AND PROPORTIONAL
RELATIONSHIPS
DIRECT PROPORTION
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The table below is a linear function.
X
1
2
3
4
Y
8
16
24
32
One way to describe the function is as x increases by one, y
increases by 8.
Another way to describe the function is by looking at the
ratio y/x in each column of the table. In each column y/x =
8.
This can be written as the equation y = 8x
Any function (linear table) that can be written as y = kx,
where k is a constant, is called a direct proportion.
DIRECT PROPORTION IN A GRAPH
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
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How can I determine if a graph is a direct
proportion?
1. The graph of a direct proportion must be a
straight line and pass through the point (0, 0).
2. Pick points on the graph and divide y by x. If
the answer is a constant (k) each time, the graph
fits the criteria for a direct proportion.
YOU TRY IT!

Scout earns $12 an hour for each hour she works.
Show that a direct proportion exists between the
number of hours she works and the amount of
money she earns.

Create a table using the information you have.

Write an equation representing the situation.

Does the equation for this problem fit the
equation for a direct proportion y = kx ?
INDIRECT PROPORTION



An indirect proportion exists when the
product (answer you get when you multiply) of
two variables is a constant (k).
For example if the variables are x and y, an
indirect proportion can be written as xy = k or
as y = k/x.
The graph of an indirect proportion will never be
a straight line.
GRAPH THE FOLLOWING COORDINATE PAIRS
(1, 8)
 (2, 4)
 (4, 2)
 (8, 1)
 Is this a direct proportion or indirect proportion?


This graph is typical of an indirect proportion.

What happens when you multiply x and y?

Each product equal 8, thus this is an indirect proportion.
YOU TRY IT!

Is the function y = 4x + 2 a direct proportion?

1st step: if x = 1, y = ?
(hint: make a table if it helps)



2nd step: what does this y/x = ?
3rd step: pick a second point. If x = 2, y = ? What does
this y/x = ?
Did you get the same answer for step 2 and 3? If so it
is a direct proportion, if not the function is not a
direct proportion.