Linear function (calculus): Difference between revisions

Revision as of 23:25, 17 September 2018

Revision as of 07:27, 28 September 2018

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In graphical terms, this gives the line <math>y=f(x)</math> with slope ''a'' passing through the point <math>(x_0,y_0)</math>.

The ''two-point form'' starts with two known values <math>f(x_0)=y_0</math> and <math>f(x_1)=y_1</math>. One computes the slope <math>a=\tfrac{y_2-y_1-y_0}{x_2-x_1-x_0}</math> and inserts this into the point-slope form:

:<math>f(x) = \tfrac{y_1-y_0}{x_1-x_0}(x{-}x_0\!) + y_0</math>.

Its graph <math>y=f(x)</math> is the unique line passing through the points <math>(x_0,y_0\!), (x_1,y_1\!)</math>. The equation <math>y=f(x)</math> may also be written to emphasize the constant slope: