Linear function (calculus): Difference between revisions

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==Slope==

[[File:Slope picture.svg|thumb|right|100px|The slope of a line is the ratio between a change in ''x'', denoted Δ''x'', and the corresponding change in ''y'', denoted Δ''y'']]

<nowiki>The [[slope (mathematics)|slope]] of a linear function tells how steeply the graph of the function is slanted. </nowiki>

The [[slope (mathematics)|slope]] of a nonvertical line is a number that measures how steeply the line is slanted. The [[first derivative]] of a linear function, in the sense of calculus, is exactly this slope of the graph of the function. For {{math|1=f(x) = ax + b}}, this slope and derivative is given by the constant {{math|1=a}}. Linear functions can be characterized as the only real-valued functions that are defined on the entire real line and have a constant derivative.

==Relationship with linear equations==