1. 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 = m1x + b1
y = m2x + b2
m1 = m2
b1 ≠ b2

2. 2. Coincident
-slopes are equal and y-intercepts are equal
m1 = m2
y = m1x + b1
b1 = b2
y = m2x + b2
-the equations are identical
-one line sits on the other
-the ordered pairs for both lines are the same

3. 3. Perpendicular
-product of slopes = -1
m1 • m2 = -1
y = m1x + b1
y = m2x + b2
-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. 4. Intersecting
-slopes are different
y = m1x + b1
m1 ≠ m2
y = m2x + b b1 ≠ b2
They are concurrent at the point (-4,-3).

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

6. = y = 2x + 5 y = 2(-4) + 5 y = -8 + 5 2(2x + 5) = 1(-5x – 26)
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 = 2x + 5 =
y = 2(-4) + 5
y =
y = -3
2(2x + 5) = 1(-5x – 26)
4x + 10 = -5x – 26
4x + 5x = -26 – 10
9x = -36
x = -4