### Parallel and Perpendicular Lines

Parallel lines are two lines in the same plane that do not intersect. Two non-vertical lines are parallel if and only if they have the same slope.

If you are given the equation of a line and a point not on that line, you can find the equation of the line through this point parallel to the given line by using the point-slope form.

Perpendicular lines are lines that intersect at right angles. Two non-vertical lines are perpendicular if and only if the product of their slopes is –1 (or, equivalently, their slopes are negative reciprocals of each other).

You can use this fact to determine whether a pairs of lines whose equations have been given are perpendicular or not.

If you are given the equation of a line and a point, you can find the equation of the line through this point perpendicular to the given line by using the point-slope form. You must first find the slope of the given line and then take its negative reciprocal.

### Parallel and Perpendicular Lines

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Parallel Lines 0:12
- Example: Non-vertical Lines
- Perpendicular lines 1:57
- Example: Slope Product is -1
- Negative Reciprocal
- Lecture Example 1 3:58
- Lecture Example 2 7:12
- Additional Example 3
- Additional Example 4

3 answers

Last reply by: Stephen Gaddis

Sun Nov 27, 2011 4:20 PM

Post by SASHKA YAKIMOVA on January 3, 2010

Is it possible instead of using shortcuts to write the complete solution step-by-step? That happened in the previous section (Point Slope Form of an Equation)as well and did not understand the example. Can somebody please explain how did you get b=5 from 9=4+b in Example 1. Thanks!