proportionality

In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant. Two sequences are inversely proportional if corresponding elements have a constant product, also called the coefficient of proportionality.
This definition is commonly extended to related varying quantities, which are often called variables. This meaning of variable is not the common meaning of the term in mathematics (see variable (mathematics)); these two different concepts share the same name for historical reasons.
Two functions



f
(
x
)


{\displaystyle f(x)}
and



g
(
x
)


{\displaystyle g(x)}
are proportional if their ratio






f
(
x
)


g
(
x
)





{\textstyle {\frac {f(x)}{g(x)}}}
is a constant function.
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).
Proportionality is closely related to linearity.

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