# 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**

**Two-point form**

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.

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