What is Proportionality: Definition and 82 Discussions

In mathematics, two varying quantities are said to be in a relation of proportionality,
multiplicatively connected to a constant; that is, when either their ratio or their product yields a constant. The value of this constant is called the coefficient of proportionality or proportionality constant.

If the ratio (y/x) of two variables (x and y) is equal to a constant (k = y/x), then the variable in the numerator of the ratio (y) can be product of the other variable and the constant (y = k ⋅ x). In this case y is said to be directly proportional to x with proportionality constant k. Equivalently one may write x = 1/k ⋅ y; that is, x is directly proportional to y with proportionality constant 1/k (= x/y). If the term proportional is connected to two variables without further qualification, generally direct proportionality can be assumed.
If the product of two variables (x ⋅ y) is equal to a constant (k = x ⋅ y), then the two are said to be inversely proportional to each other with the proportionality constant k. Equivalently, both variables are directly proportional to the reciprocal of the respective other with proportionality constant k (x = k ⋅ 1/y and y = k ⋅ 1/x).If several pairs of variables share the same direct proportionality constant, the equation expressing the equality of these ratios is called a proportion, e.g., a/b = x/y = ... = k (for details see Ratio).

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