1. Parallel, Perpendicular, and Oblique Lines
Using Coordinate Geometry to Find and Compare the Slopes of Lines

2. Parallel Lines
Two lines are Parallel if they lie in the same plane and do not intersect

3. Perpendicular Lines
Two lines are Perpendicular if they intersect at a right (90°)

4. Oblique Lines
Two lines are Oblique if they lie in the same plane but are neither Perpendicular nor Parallel

5. Skew Lines
Two lines are Skew if they do not lie in the same plane

6. Slope
Recall that slope = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 , so draw in a slope triangle to find the rise and run l 3 4
𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 8 6 = 4 3 6 8

7. Parallel Lines Slope of line l = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 4 3 Slope of line m
Since Parallel lines never intersect but lie in the same plane, they must have the same slope
Slope of line l
= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 4 3 l m 3 3 4 4
Slope of line m
= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 4 3

8. Perpendicular Lines Slope of line l = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 4 3 Slope of line n
Since Perpendicular lines intersect at right angles, there slopes are opposite reciprocals
Slope of line l
= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 4 3 l 3 n 4 -3
Slope of line n
= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = −3 4 4

9. Oblique Lines Slope of line l = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 4 3 Slope of line q
Since Oblique lines are neither parallel nor perpendicular, there slopes are not equal, nor opposite reciprocals
Slope of line l
= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 4 3 l 3 q 4 -3
Slope of line q
= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = −3 7 7

10. Review Parallel Lines Never intersect Same Slope Perpendicular Lines
Intersect at a Right Angle
Opposite Reciprocal Slope
Oblique Lines
intersect at a non-right angle
Non-equal and non-opposite recriprocal slopes