Editing Proportionality (mathematics) (section)

{{Short description|Property of two varying quantities with a constant ratio}}
{{Other uses|Proportionality (disambiguation){{!}}Proportionality}}
{{more footnotes needed|date=August 2021}}
[[File:Proportional variables.svg|thumb|300x300px|The variable ''y'' is directly proportional to the variable ''x'' with proportionality constant ~0.6.]]
[[File:Inverse proportionality function plot.gif|thumb|300x300px|The variable ''y'' is inversely proportional to the variable ''x'' with proportionality constant 1.]]

In [[mathematics]], two [[sequence]]s of numbers, often [[experimental data]], are '''proportional''' or '''directly proportional''' if their corresponding elements have a [[Constant (mathematics)|constant]] [[ratio]]. The ratio is called '''''coefficient of proportionality''''' (or '''''proportionality constant''''') and its reciprocal is known as '''''constant of normalization''''' (or '''''normalizing constant'''''). Two sequences are '''inversely proportional''' if corresponding elements have a constant product.

Two [[function (mathematics)|functions]] <math>f(x)</math> and <math>g(x)</math> are ''proportional'' if their ratio <math display=inline>\frac{f(x)}{g(x)}</math> 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., {{math|1={{sfrac|''a''|''b''}} = {{sfrac|''x''|''y''}} = ⋯ = ''k''}} (for details see [[Ratio]]).
Proportionality is closely related to ''[[linearity]]''.