What is Linear function?
{{Distinguish| Linear equation}} [[File:line gen m no slope.svg|thumb|right|Linear function (The line here is ''generic''. It is slanted so ''m''&ne;0. See examples with actual values for ''m'' and ''b'' below.)]] In basic mathematics, a '''linear function''' is a [[Function (mathematics)|function]] whose [[:wikt:graph|graph]] is a [[Line|straight line]] in 2-dimensions (2D, see images).<ref>{{cite book| last1 = Gelfand| first1 = I.M.| last2 = Glagoleva| first2 = E.G.| last3 = Shnol| first3 = E.E.| title = Functions and Graphs| year = 1990| publisher = Dover Publications| isbn = 978-0-486-31713-7| page = 22 }} {{in lang|en}}</ref> An example is: ''y''=2''x''&ndash;1. In higher mathematics, a linear function often refers to a [[linear mapping]].<ref>{{cite web|url=http://cfsv.synechism.org/c1/sec15.pdf|title=The Calculus of Functions of Several Variables, Linear and Affine Functions|last1=Sloughter|first1=Dan|year=2001|language=en|access-date=1 February 2014}}</ref><ref>{{cite web|url=http://mathworld.wolfram.com/LinearFunction.html|last1=Rowland|first1=Todd|title=Linear function (mathematics)|publisher=From MathWorld--A Wolfram Web Resource|language=en|access-date=1 January 2014}}</ref> ==Basic Properties== Formally, a linear function is a function ''f''(''x''):'''R'''→'''R''' such that the graph of ''f'' is a line. This means the [[function (mathematics)|domain]] or input of ''f'' is a [[real number]] '''R''' and the [[function (mathematics)|range]] or output of ''f'' is also a real number '''R'''. Usually we write ''y''(''x'') or just ''y'' in place of ''f''(''x''). So the formal statement means: * we input or substitute a real number ''x'' into the linear function * the linear function outputs or gives a real number ''y'' and * all of these points (''x'',''y'') make a line. There are three main forms for writing linear functions: '''slope-intercept''', '''standard''' and '''parametric'''. [[File:line explicit ex.svg|thumb|right|Slope-intercept form of a line (unique)]] ===Slope-intercept form=== The '''sl