Consider the side length of an equilateral triangle as (in ) and its perimeter as (in ):
1
2
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3
6
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x 1 2 3 4 5 6 cdots
y 3 6 9 12 15 18 cdots
If doubles, triples, quadruples, and so on, and also doubles, triples, quadruples, etc., then is said to be directly proportional to .
The relationship between and can be expressed as .
In general, if is directly proportional to , the relationship between and can be written as:
Graph of a Direct Proportionality
When can take any real value, the graph of a direct proportionality has the following properties:
Properties of the Graph for
The graph of a direct proportionality is a straight line that passes through the origin.
When :
The graph passes through the 1st and 3rd quadrants.
When :
The graph passes through the 2nd and 4th quadrants.
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