## Product of linear equations

Simple patterns, variables, the order of operations, simplification, evaluation, linear equations and graphs, etc.
AsgerJon
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Joined: Sat Mar 12, 2011 1:47 am
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### Product of linear equations

Consider lines l and m. Imagine that they intersect each other and form a 90° angle between them. In this situation the product of the gradients from each line is equal to -1.

l: y = ax+b
m: y = mx+n

l and m form a 90° angle. (I don't know the precise English linguistics describing such a situation, please enlighten me).
Therefore:
a * m = -1

Here's what I can't figure out: How do I setup a proof of the above? I mean I can prove that a * m will be negative, because if the two lines form a 90° angle then the two lines can't be both positive nor negative, they have to be one of each, which will always yield a negative number. I can also see in my head that if m is 2 then a must be negative and 1 divided by m.

I need to be able to write QED at the end, can someone help me please?

stapel_eliz
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I think you are asking how to prove that perpendicular lines have slopes which are negative reciprocals and whose products are equal to -1. If so, then there are various ways of proving this statement. However, I do not think a knowledge of pre-algebra (the category to which you have posted your question) will be sufficient. For instance:

The Math Page: Slope of a line
Slopes of Parallel and Perpendicular Lines
Why Slopes of Perpendicular Lines are Negative Reciprocals
Analyze Math: Slopes of Two Perpendicular Lines
Ask Dr. Math: Slopes of Perpendicular Lines

Good luck!

AsgerJon
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Joined: Sat Mar 12, 2011 1:47 am
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### Re: Product of linear equations

I'm in college in Denmark, and we are going through a lot of math this semester. I have most of it down, I just have a few blank spot, this situation with, and I quote:
perpendicular lines have slopes which are negative reciprocals and whose products are equal to -1
, but I guess it's not as simple to prove as I thought. Well, it's good to know that I wasn't missing anything obvious.

One last question, why can't I have a signature?

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### Re: Product of linear equations

...why can't I have a signature?
Unfortunately, many spammers use signatures for posting illicit links.

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
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### Re: Product of linear equations

...why can't I have a signature?
Unfortunately, many spammers use signatures for posting illicit links.
Only people that have over 300 posts should have a signature.