Proportionality (mathematics)

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This article is about proportionality, the mathematical relation. For other uses of the term proportionality, see proportionality (disambiguation).

In mathematics, two related quantities x and y are called proportional (or directly proportional) if there exists a constant non-zero number k such that

<math>y = k x<math>.

In this case, k is called the proportionality constant of the relation. If y and x are proportional, we often write

<math>y \sim x<math> or <math>y \propto x<math>.

For example, if you travel at a constant speed, then the distance you cover and the time you spend are proportional, the proportionality constant being the speed. Similarly, the amount of force acting on a certain object from the gravity of the Earth at sea level is proportional to the object's mass.

To test whether x and y are proportional, one performs several measurements and plots the resulting points in a Cartesian coordinate system. If the points lie on (or close to) a straight line passing through the origin (0,0), then the two variables are proportional, with the proportionality constant given by the line's slope.

The two quantities x and y are inversely proportional if there exists a non-zero constant k such that

<math>y = {k \over x}<math>.

For instance, the number of people you hire to shovel sand is (approximately) inversely proportional to the time needed to get the job done.

Proportionality (mathematics)

See also