Editing Proportionality (mathematics) (section)

== Inverse proportionality ==
[[File:Inverse proportionality function plot.gif|thumb|300x300px|Inverse proportionality with product {{nowrap|1=''x y'' = 1 .}}]]

Two variables are '''inversely proportional''' (also called '''varying inversely''', in '''inverse variation''', in '''inverse proportion''')<ref>{{cite web | url=https://www.math.net/inverse-variation |title=Inverse variation |website=math.net |access-date=October 31, 2021}}</ref> if each of the variables is directly proportional to the [[multiplicative inverse]] (reciprocal) of the other, or equivalently if their [[Product (mathematics)|product]] is a constant.<ref>Weisstein, Eric W. [http://mathworld.wolfram.com/InverselyProportional.html "Inversely Proportional"]. ''MathWorld'' – A Wolfram Web Resource.</ref> It follows that the variable ''y'' is inversely proportional to the variable ''x'' if there exists a non-zero constant ''k'' such that
: <math>y = \frac{k}{x}</math>
or equivalently, <math>xy = k</math>. Hence the constant "''k''" is the product of ''x'' and ''y''.

The graph of two variables varying inversely on the [[Cartesian coordinate]] plane is a [[rectangular hyperbola]]. The product of the ''x'' and ''y'' values of each point on the curve equals the constant of proportionality (''k''). Since neither ''x'' nor ''y'' can equal zero (because ''k'' is non-zero), the graph never crosses either axis.

Direct and inverse proportion contrast as follows: in direct proportion the variables increase or decrease together. With inverse proportion, an increase in one variable is associated with a decrease in the other. For instance, in travel, a constant speed dictates a direct proportion between distance and time travelled; in contrast, for a given distance (the constant), the time of travel is inversely proportional to speed: ''s''  × ''t'' = ''d''.