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# 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?
• This whole topic of negative inverses of slopes, is this explained in more detail on Khan Academy?
• Could you have lines that are both parallel and perpendicular ?
• no because perpendicular lines always intersect .parallel lines never intersect
(1 vote)
• 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)
• in the 2nd one why do I divide -12/8 by 4?
• the reason he did that is he simplified the fraction, to get a better example of what the fraction is to decimal form.
(1 vote)
• Is there a formula to find where two lines intersect based on their equations?
(1 vote)
• It means there is no solution between two equations if two lines are parallel, but are there any benefits in knowing two lines are perpendicular?
(1 vote)
• Yes, because by knowing 2 lines are perpendicular, you know the angle between them is a right angle (90 degree). This is really important for a lot of geometry problems.

For example, you have 3 lines forming a triangle. By knowing 2 of them are perpendicular to each other, you will know that this triangle is a right triangle. Thus you can use trigonometry or Pythagorean's Theorem on this triangle.

Another example is a theorem stating that if you have a circle and an inscribed triangle inside this circle, if this triangle is right triangle, then the opposite side of this right angle is the diameter. Now checking perpendicular becomes handy if you want to find the area of the circle etc.

Also, if you have an isosceles triangle ABC where AB = AC. Now suppose you have a line from A onto BC, and you would like to know that is this line the perpendicular bisector of this triangle. Since property of isosceles triangle states that if this line is perpendicular to BC, then this is the altitude and the bisector of BC, you can once again use your knowledge on finding perpendicular lines.