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

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.

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.

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

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

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.

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)