Difference between revisions of "Proportion"
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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. | 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. | ||
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The graph of a direct proportion is always [[line]]ar. | The graph of a direct proportion is always [[line]]ar. | ||
| − | Often, this will be written as <math> | + | Often, this will be written as <math>y \propto x</math>. |
==Inverse proportion== | ==Inverse proportion== | ||
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==Problems== | ==Problems== | ||
===Introductory=== | ===Introductory=== | ||
| − | *Suppose <math> | + | *Suppose <math>\frac{1}{20}</math> is either '''x''' or '''y''' in the following system:<br /> |
:<math>\begin{cases} | :<math>\begin{cases} | ||
xy=\frac{1}{k}\\ | xy=\frac{1}{k}\\ | ||
Revision as of 18:56, 20 September 2007
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.
Contents
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:
where k is some real number.
The graph of a direct proportion is always linear.
Often, this will be written as 
.
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:
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
A proportion in which one number is equal to a constant raised to the power of the other, or the logarithm of the other, is called an exponential proportion. It can be expressed as either:
or
or
for some real number k, where k is not zero or one.
Problems
Introductory
- Suppose
is either x or y in the following system:
is either x or y in the following system:
Find the possible values of k. (Source)
