1. Ways to represent them Their uses
Lines in the plane
Ways to represent them
Their uses

2. We define the line in the coordinate plane through points A=(a1,a2)
and B=(b1,b2) to be all points (x,y) such that
(x,y) = (B-A)t + A = ( (b1-a1)t + a1, (b2-a2)t + a2) for some t
Problem: Find parametric equations for the line through (2,5) at t=0
and (4,-3) at t = 1.

3. Eliminating the parameter:
Suppose a line L is given by the parametric equations
x = 3t +2, y = -5t -4
Problem. Find a single equation in x and y of the form
ax + by = c which describes the line.

4. Slope of a non vertical line:
Intercepts of a line:

5. Slope-intercept form of a line:
Point-slope form of a line:

6. Problem: Given two lines, find their point(s) of intersection
Common#3 Line1: x = 1-t, y = -t +2, Line 2: 4y -3x + 1 = 0
Common#6 Line1: -2y -6x + 2 = 0 Line2: -2y -5x + 2 = 0
Line3: 2y – 6x + 2 = 0. Find each pairwise intersection.

7. Reflecting lines off the x-axis: Suppose a pool ball at (5, 10) is shot
towards the point (3, 0) on x-axis. If it bounces off the x-axis at the
same angle it hits at, where will it hit the y-axis? (this is like common
#4)