Equation of Line
\(y = mx + c\)
\(m\) is a gradient and \(c\) is y-intercept
Gradient
1. Gradient of angle to the x-axis
\(m = \tan \alpha\)
2. Gradient of two points
\(m = \dfrac {y_2 - y_1}{x_2 - x_1}\)
Equation of Line
1. Gradient and one point
\(y - y_1 = m \:.\: (x - x_1)\)
2. Two points
\(\dfrac {y - y_1}{y_2 - y_1} = \dfrac {x - x_1}{x_2 - x_1}\)
Relations between two lines
Two parallel lines
\(m_1 = m_2\)
Two perpendicular lines
\(m_1 \:.\: m_2 = -1\)
Midpoint and Distance
Midpoint
\(M = \dfrac {(x_1 + x_2, \: y_1 + y_2)}{2}\)
Distance between two points
\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
Exercise