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==Slope-intercept, point-slope, and two-point forms==
A given linear function <math>\ellf(x)</math> can be written in several standard formulas displaying its various properties. The simplest is the ''slope-intercept form'':
:<math>\ellf(x)= mxax+b</math>,
from which one can immediately see the slope ''ma'' and the initial value <math>\ellf(0)=b</math>, which is the ''y''-intercept of the graph <math>y=\ell(x)</math>.
Given a slope ''ma'' and aone known value <math>\ellf(ax_0)=by_0</math>, onewe writeswrite the ''point-slope form'':
:<math>\ellf(x) = ma(x{-}ax_0)+by_0</math>.
In graphical terms, this gives the line <math>y=\ellf(x)</math> with slope ''ma'' passing through the point <math>(ax_0,by_0)</math>.
The ''two-point form'' starts with two known values <math>\ellf(a_1x_0)=b_1y_0</math> and <math>\ellf(a_2x_1)=b_2y_1</math>. One computes the slope <math>ma=\tfrac{b_2y_2-b_1y_1}{a_2x_2-a_1x_1}</math> and inserts this into the point-slope form:
:<math>\ellf(x) = \tfrac{b_2y_1-b_1y_0}{a_2x_1-a_1x_0}(x{-}a_1x_0\!) + b_1y_0</math>.
Its graph <math>y=\ellf(x)</math> is the unique line passing through the points <math>(a_1x_0,b_1y_0\!), (a_2x_1,b_2y_1\!)</math>. ThisThe equation <math>y=f(x)</math> may also be written to emphasize the constant slope:
:<math>\frac{y-b_1y_0}{x-a_1x_0}=\frac{b_2y_1-b_1y_0}{a_2x_1-a_1x_0}</math>.
==Relationship with linear equations==
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