information:classification
Slope-intercept, point-slope, and two-point forms

A given linear function f (x) {\displaystyle f(x)} can be written in several standard formulas displaying its various properties. The simplest is the slope-intercept form:

from which one can immediately see the slope a and the initial value f (0) = b {\displaystyle f(0)=b}, which is the y -intercept of the graph y = f (x) {\displaystyle y=f(x)}.

Given a slope a and one known value f (x 0) = y 0 {\displaystyle f(x_{0})=y_{0}}, we write the point-slope form:

In graphical terms, this gives the line y = f (x) {\displaystyle y=f(x)} with slope a passing through the point (x 0, y 0) {\displaystyle (x_{0},y_{0})}.

The two-point form starts with two known values f (x 0) = y 0 {\displaystyle f(x_{0})=y_{0}} and f (x 1) = y 1 {\displaystyle f(x_{1})=y_{1}}. One computes the slope a = y 1 − y 0 x 1 − x 0 {\displaystyle a={\tfrac {y_{1}-y_{0}}{x_{1}-x_{0}}}} and inserts this into the point-slope form:

Its graph y = f (x) {\displaystyle y=f(x)} is the unique line passing through the points (x 0, y 0), (x 1, y 1) {\displaystyle (x_{0},y_{0}\!),(x_{1},y_{1}\!)}. The equation y = f (x) {\displaystyle y=f(x)} may also be written to emphasize the constant slope: