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

In mathematics, two variables are proportional if a change in one is always accompanied by a change in the other, and if the changes are always related by use of a constant multiplier. The constant is called the coefficient of proportionality or proportionality constant.

  • If one variable is always the product of the other and a constant, the two are said to be directly proportional. x and y are directly proportional if the ratio \tfrac yx is constant.
  • If the product of the two variables is always equal to a constant, the two are said to be inversely proportional. x and y are inversely proportional if the product xy is constant.

To express the statement, "y is proportional to x," we write as an equation y = cx, for some real constant c. Symbolically, we write y ∝ x.

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

If a linear function transforms 0, a and b into 0, c and d, and if the product a b c d is not zero, we say a and b are proportional to c and d. An equality of two ratios such as \tfrac ac\ =\ \tfrac bd, where no term is zero, is called a proportion.


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