The Straight Line

Definition
Straight line is the locus or path of a point that moves without changing its direction.
 

straight-line-01.jpg

 

General Equation
The general equation of the straight line is given by

$ax + by + c = 0$

 

Standard Equations

Two-point form
Given two points on the line
straight-line-02.jpg
$y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1)$

 

Point-slope form
Given a point on the line and the slope of the line.
straight-line-03.jpg

$y - y_1 = m(x - x_1)$

 

Slope-intercept form
Given the slope and y-intercept of the line.
straight-line-04.gif

$y = mx + b$

 

Intercept form
Given the x- and y-intercepts of the line.
straight-line-05.jpg

$\dfrac{x}{a} + \dfrac{y}{b} = 1$

 

Normal form
Given its normal through the origin.
straight-line-06.jpg

$x \cos \theta + y \sin \theta = p$

 

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