14.1 Lines

Representation: two points

|| --
|| •---
y-intercept | ---- |(x2,y2)
---|--- |
(x1,y1) ------------|
----•----|------------||-
-- |

Line-intercept form:

non-vertical:	y = mx + b
vertical:	x = c

Slop m: $y -y x22-x11$
Y-intercept: b = y₁ - mx₁

Proof. $-b--y1 m = 0- x1$

Linear-equation form: ax + by + c = 0

Intersecting lines:

y	=	m₁x + b₁
y	=	m₂x + b₂

x=...
y=...
tan angle: $m = -m2-m1- m1m2 -1$

Proof. ?

|--
........ ---(1,m2)
.......... --- |
.........- |
--- .......m- |
--- ......--
--- (1,m1....)...-----
--- --------.......- ---
----------- ..... ---
----------------------......--------
- ....

Perpendicular lines

y = mx1 + b y = - m-x + b