# Linearity **Linearity** is the property of a mathematical relationship (function) that can be graphically represented as a straight line. This initial, visual relationship needed to be formalized, so we came up with two properties that a linear relationship would always satisfy. Given a map $f(x)$, $f$ is linear if it satisfies the two properties: * **Additivity**: $f(x + y) = f(x) + f(y)$ * **Homogeneity of degree 1**: $f(ax) = a f(x) \;\; \forall \;\; a$ --- Links to: [Linear Transformations](Linear%20Transformations.md) [Operators](Operators.md) [Does Linearity provide Information](Does%20Linearity%20provide%20Information.md) References: * https://en.wikipedia.org/wiki/Linearity