Slopes of Parallel and Perpendicular Lines

1. Slopes of Parallel and Perpendicular Lines Recall that two lines are parallel if they are in the same plane and do not intersect. Two lines are perpendicular if they intersect at a right angle

2. Example 1: Consider the following graph with two lines that are parallel. Since both lines have the same “steepness”, their slopes must be the same value.

3. Example 2: Consider the following graph with two lines that are perpendicular. Notice that the line in red has a positive slope (rising), while the line in blue has a negative slope (falling).

6. This is a quite interesting result. Not only are the slopes opposite in sign, but they are reciprocals! As it turns out, this is always the case, assuming that neither line is vertical, which has undefined slope.

7. Example 3: Special case #1 When both lines are vertical, they are parallel. Recall that vertical lines have undefined slope. Thus, …

8. Example 4: Special case #2 When one line is vertical, and the other is horizontal, then the lines are perpendicular. The slope of the vertical line is undefined … … and the slope of the horizontal line is zero.

9. SUMMARY (assume no vertical lines) Parallel lines Perpendicular lines Slopes are opposite reciprocals Slopes are the same

10. Example 5: Line 1 has a slope of – 3. a) Determine the slope of Line 2 that is parallel to Line 1 b) Determine the slope of Line 3 if it is perpendicular to Line 1

11. Example 6: Line 1 has a slope of 3/4. a) Determine the slope of Line 2 that is parallel to Line 1

12. Line 1 has a slope of 3/4. b) Determine the slope of Line 3 if it is perpendicular to Line 1

13. While we have written out all the details, these problems are usually done in your head. For part b again … Use two steps: 1) The reciprocal is: 2) Take the opposite:

14. END OF PRESENTATION