Straight Lines

$m = tan(\theta) = (y2-y1)/(x2-x1)$

$\theta =$ angle of inclination $(0 \leq \theta < 180, \theta \neq 90). m$ is undefined for vertical lines.

$y = mx + c$

$m =$ slope, $c = y-intercept$ (where line crosses $y-axis).$

$y - y1 = m(x - x1)$

Line through $(x1,y1)$ with slope m.

$(y-y1)/(y2-y1) = (x-x1)/(x2-x1)$

Equation of line through $(x1,y1)$ and $(x2,y2).$

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

$a = x-intercept, b = y-intercept.$ Valid when $a \neq 0$ and $b \neq 0.$

$x*cos(\omega) + y*sin(\omega) = p$

$p =$ perpendicular distance from origin, $\omega =$ angle normal makes with positive $x-axis (p > 0).$

$ax + by + c = 0$

Most general equation of a straight line. Slope $= -\frac{a}{b}, y-intercept = -\frac{c}{b}.$

$d = |ax1 + by1 + c| / \sqrt{a^2 + b^2}$

Distance from point $(x1,y1)$ to line $ax+by+c=0.$

$tan(\theta) = |(m1-m2)/(1+m1*m2)|$

$\theta$ is the acute angle between lines with slopes $m1$ and $m2.$

$L1 + \lambda*L2 = 0 represents all lines through intersection of L1=0 and L2=0$

Any line through the intersection of $L1$ and $L2$ can be written as $L1 + \lambda*L2 = 0$ for some $\lambda.$