Difference between revisions of "Proportion"

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<math>xy=k</math><br />
 
<math>xy=k</math><br />
 
where k is some real number that does not equal zero. <br />
 
where k is some real number that does not equal zero. <br />
 +
The graph of an inverse proportion is always a hyperbola, with asymptotes at the x and y axes. <br />
  
 
==Exponential Proportion==
 
==Exponential Proportion==

Revision as of 20:24, 13 September 2007

This is an AoPSWiki Word of the Week for Sep 13-19

Two numbers are said to be in proportion to each other if some numeric relationship exists between them. There are several types of proportions, each defined by a separate class of function.

Direct Proportion

Direct proportion is a proportion in which one number is a multiple of the other. Direct proportion between two numbers x and y can be expressed as:
$y=kx$
where k is some real number.
The graph of a direct proportion is always linear.

Inverse Proportion

Inverse proportion is a proportion in which as one number's absolute value increases, the other's decreases in a directly proportional amount. It can be expressed as:
$xy=k$
where k is some real number that does not equal zero.
The graph of an inverse proportion is always a hyperbola, with asymptotes at the x and y axes.

Exponential Proportion