If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Geometry (FL B.E.S.T.)

### Course: Geometry (FL B.E.S.T.)>Unit 5

Lesson 6: Parallel & perpendicular lines on the coordinate plane

# Parallel & perpendicular lines from graph

The slopes of parallel lines are equal, and the slopes of perpendicular lines are opposite reciprocals. This is a worked example of determining whether given lines are parallel or perpendicular.

## Want to join the conversation?

• At Sal says slope but writes M. Why?
• That's a good question.

I did some internet research. I found that according to http://mathworld.wolfram.com/Slope.html , it is not known for sure why slope is called m but perhaps it's because "climb" in English translates to "montar" in French.

Have a blessed, wonderful day!
• Why does sal subtract -3-0 when the slope formula is y2-y1/ x2-x1 .
Shouldn’t it be 0-(-3)
• It's fine either way, wether you start from x1,y1 or x2,y2. Just think of them as a ratio of height to the base to determine the "slope".
• is math related to science?
• Sometimes, Math is separated into theoretical and practical, much of what you learn in school math classes is theoretical, but word problems often attempt to move from theoretical to practical. Much of science is related to the practical aspects of math, but not all of science is math related.
• At there is a fraction over a fraction i always get confused with these.Is there any video available in khan academy or an article for explanation?
• Could you have lines that are both parallel and perpendicular ?
• no because perpendicular lines always intersect .parallel lines never intersect
(1 vote)
• This whole topic of negative inverses of slopes, is this explained in more detail on Khan Academy?
• why is it so that the multiplication of the gradients of both lines which are perpendicular to each other is equivalent to -1? How do you prove this?
(1 vote)
• x-4=6y
I do not want the straight answer. If anyone can, could you explain the steps to do this? And why we do that certain step, if that makes sense?
I appreciate it!
(1 vote)
• If we try to find parallel and perpendicular lines for this line, we have to find its slope. This is because parallel lines will all have the same slope as the line, while perpendicular lines will all have the opposite reciprocal slope. To find the slope of this line, we can convert it to slope-intercept form (which looks like y = mx + b where m is the slope):
x - 4 = 6y
y = (x - 4) / 6
y = 1/6 x - 2/3
The slope of the line is 1/6. Parallel lines to this would have the same slope, 1/6 as well. The equations to those lines would then be y = 1/6x + b, where b could be any y-intercept. This is because no matter how much you move the parallel line up or down, its slope will be the same so it will still be parallel.
Perpendicular lines have the opposite reciprocal slope. So instead of 1/6, we have the reciprocal, 6/1, and the opposite of that, -6 for the slope.
• in the 2nd one why do I divide -12/8 by 4?