Equation of line

$y = m x + c$

$m$ is a gradient and $c$ is y-intercept

Gradient

1. Gradient of angle to the x-axis

$m = \tan α$

2. Gradient of two points

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Equation of Line

1. Gradient and one point

$y - y_{1} = m . (x - x_{1})$

2. Two points

$\frac{y - y_{1}}{y_{2} - y_{1}} = \frac{x - x_{1}}{x_{2} - x_{1}}$

Relations between two lines

Two parallel lines

$m_{1} = m_{2}$

Two perpendicular lines

$m_{1} . m_{2} = - 1$

Midpoint and Distance

Midpoint

$M = \frac{(x_{1} + x_{2}, y_{1} + y_{2})}{2}$

Distance between two points

$d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$