Lines can be classified four different ways according

Lines can be classified four different ways according to their relationship to each other. Classification of lines: 1. Parallel and Distinct -slopes are equal and y-intercepts are different y = m 1 x + b 1 y = m 2 x + b 2 m 1 = m 2 b 1 ≠ b 2

2. Coincident -slopes are equal and y-intercepts are equal y = m 1 x + b 1 y = m 2 x + b 2 m 1 = m 2 b 1 = b 2 -the equations are identical -one line sits on the other -the ordered pairs for both lines are the same

3. Perpendicular -product of slopes = -1 y = m 1 x + b 1 m 1 • m 2 = -1 y = m 2 x + b 2 -slopes are negative reciprocals of each other -because slopes are different the lines are intersecting All perpendicular lines are also concurrent. These two lines are concurrent at (5, 0).

4. Intersecting -slopes are different y = m 1 x + b 1 m 1 ≠ m 2 y = m 2 x + b 2 b 1 ≠ b 2 They are concurrent at the point -4, -3). (

4. Intersecting cont’d y = 2 x + 5 When 2 lines are intersecting, the point of intersection, when substituted for x and y in both equations will make them true statements. y = 2 x + 5 -3 = 2(-4) + 5 -3 = -8 + 5 -3 = -3 -3 -4 (-4, -3)

Not only can we prove that a point belongs to both lines but if we have both equations, we can determine the point of intersection. y = 2 x + 5 = 2(2 x + 5) = 1(-5 x – 26) 4 x + 10 = -5 x – 26 4 x + 5 x = -26 – 10 9 x = -36 x = -4 y = 2(-4) + 5 y = -8 + 5 y = -3