This document provides 32 examples of finding the equations of lines parallel or perpendicular to a given line through a given point. It examines scenarios where the given point is in each quadrant of the coordinate plane and where the given point lies on one of the axes, while the original line has either a positive or negative slope. Each of the 32 examples solves a different variation of these line scenarios.

1. Equations of Parallel and
Perpendicular Lines

2. Overview
This set of tutorials provides 32 examples
of finding the equations of lines parallel or
perpendicular to a given line through a
given point.

3. Example 1: Point in Q1 parallel to line with positive slope

4. Example 2: A point in Q1 perpendicular to a line with positive slope

5. Example 3: Point in Q1 parallel to line with negative slope

6. Example 4: Point in Q1 perpendicular to line with negative slope

7. Example 5: Point in Q2 parallel to line with positive slope

8. Example 6: Point in Q2 perpendicular to line with positive slope

9. Example 7: Point in Q2 parallel to line with negative slope

10. Example 8: Point in Q2 perpendicular to line with negative slope

11. Example 9: Point in Q3 parallel to line with positive slope

12. Example 10: Point in Q3 perpendicular to line with positive slope

13. Example 11: Point in Q3 parallel to line with negative slope

14. Example 12: Point in Q3 perpendicular to line with negative slope

15. Example 13: Point in Q4 parallel to line with positive slope

16. Example 14: Point in Q4 perpendicular to line with positive slope

17. Example 15: Point in Q4 parallel to line with negative slope

18. Example 16: Point in Q4 perpendicular to line with negative slope

19. Example 17: Point on the positive x-axis parallel to line with
positive slope

20. Example 18: Point on the positive x-axis perpendicular to line with
positive slope

21. Example 19: Point on the positive x-axis parallel to line with
negative slope

22. Example 20: Point on the positive x-axis perpendicular to line with
negative slope

23. Example 21: Point on the negative x-axis parallel to line with
positive slope

24. Example 22: Point on the negative x-axis perpendicular to line with
positive slope

25. Example 23: Point on the negative x-axis parallel to line with
negative slope

26. Example 24: Point on the negative x-axis perpendicular to line with
negative slope

27. Example 25: Point on the positive y-axis parallel to line with
positive slope

28. Example 26: Point on the positive y-axis perpendicular to line with
positive slope

29. Example 27: Point on the positive y-axis parallel to line with
negative slope

30. Example 28: Point on the positive y-axis perpendicular to line with
negative slope

31. Example 29: Point on the negative y-axis parallel to line with
positive slope

32. Example 30: Point on the negative y-axis perpendicular to line with
positive slope

33. Example 31: Point on the negative y-axis parallel to line with
negative slope

34. Example 32: Point on the negative y-axis perpendicular to line with
negative slope