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In [[differential calculus|calculus]], the derivative of a general function measures its rate of change. A linear function <math>f(x)=ax+b</math> has a constant rate of change equal to its slope {{mvar|a}}, so its derivative is the constant function <math>f\,'(x)=a</math>.
The fundamental idea of differential calculus is that any [[differentiable function|smooth]] function <math>f(x)</math> (not necessarily linear) can be closely [[linear approximation|approximated]] near a given point <math>x=c</math> by a unique linear function. The [[derivative]] <math>f\,'(c)</math> is the slope of this linear function, and the approximation is: <math>f(x) \approx f\,'(c)(x{-}c)+f(c)</math> for <math>x\approx c</math>. The graph of the linear approximation is the [[tangent line]] of the graph <math>y=f(x)</math> at the point <math>(c,f(c))</math>. The derivative slope <math>f\,'(c)</math> generally varies with the point ''c''. Linear functions can be characterized as the only real functions whose derivative is constant: if <math>f\,'(x)=a</math> for all ''x'', then <math>f(x)=ax+b</math> for <math>b=f(0)</math>.
==Slope-intercept, point-slope, and two-point forms==
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* James Stewart (2012), ''Calculus: Early Transcendentals'', edition 7E, Brooks/Cole. {{isbn|978-0-538-49790-9}}
* {{citation|first=Earl W.|last=Swokowski|title=Calculus with analytic geometry|edition=Alternate|year=1983|publisher=Prindle, Weber & Schmidt|place=Boston|isbn=0871503417|url-access=registration|url=https://archive.org/details/calculuswithanal00swok}}
== External links ==
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