The Straight Line
Definition
Straight line is the locus or path of a point that moves without changing its direction.
General Equation
The general equation of the straight line is given by
$ax + by + c = 0$
Standard Equations
Given two points on the line
$y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1)$
Point-slope form
Given a point on the line and the slope of the line.
$y - y_1 = m(x - x_1)$
Slope-intercept form
Given the slope and y-intercept of the line.
$y = mx + b$
Intercept form
Given the x- and y-intercepts of the line.
$\dfrac{x}{a} + \dfrac{y}{b} = 1$
Normal form
Given its normal through the origin.
$x \cos \theta + y \sin \theta = p$
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