Straight Lines — Formula Sheet

y = mx + c

y - y₁ = m(x - x₁)

y - y₁ = \frac{y₂ - y₁}{x₂ - x₁}(x - x₁)

\frac{x}{a} + \frac{y}{b} = 1

x \cos \alpha + y \sin \alpha = p

\tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right|

d = \left| \frac{Ax_1 + By_1 + C}{\sqrt{A^2 + B^2}} \right|

\frac{|c_1 - c_2|}{\sqrt{a^2 + b^2}}

\frac{h - x_1}{a} = \frac{k - y_1}{b} = -\frac{ax_1 + by_1 + c}{a^2 + b^2}

\frac{h - x_1}{a} = \frac{k - y_1}{b} = -\frac{2(ax_1 + by_1 + c)}{a^2 + b^2}

L₁ + λL₂ = 0

If the line passes through origin, $ b = 0 $ or $ c = 0 $ respectively.

Lines are parallel if $ m_1 = m_2 $, and perpendicular if $ m_1 m_2 = -1 $.

In general form, lines $ A_1x + B_1y + C_1 = 0 $ and $ A_2x + B_2y + C_2 = 0 $ are perpendicular if $ A_1A_2 + B_1B_2 = 0 $.

The equation x/a + y/b = 1 represents a line that cuts the x-axis at (a, 0) and y-axis at (0, b).