Proportional (mathematics)

In mathematics, two variables are proportional if there is always a constant ratio between them. The constant is called the coefficient of proportionality or proportionality constant.

To express the statement "y is directly proportional to x" mathematically, we write an equation y = cx, where c is the proportionality constant. Symbolically, this is written as y ∝ x.

To express the statement "y is inversely proportional to x" mathematically, we write an equation y = c/x. We can equivalently write "y is directly proportional to 1/x".

Given two variables x and y, y is directly proportional to x if there is a non-zero constant k such that

See also: Equals sign

The relation is often denoted, using the ∝ or ~ symbol, as

and the constant ratio

is called the proportionality constant, constant of variation or constant of proportionality. This can also be viewed as a two-variable linear equation with a Y-intercept of 0.

Since

is equivalent to

it follows that if y is directly proportional to x, with (nonzero) proportionality constant k, then x is also directly proportional to y, with proportionality constant 1/k.

If y is directly proportional to x, then the graph of y as a function of x is a straight line passing through the origin with the slope of the line equal to the constant of proportionality: it corresponds to linear growth.

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