Product of linear equations  TOPIC_SOLVED

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Product of linear equations

Postby AsgerJon on Sat Mar 12, 2011 2:50 am

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? :D
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Postby stapel_eliz on Sat Mar 12, 2011 2:21 pm

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! :wink:
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Re: Product of linear equations

Postby AsgerJon on Sat Mar 12, 2011 8:52 pm

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

Postby PM_Admin on Sat Mar 12, 2011 9:10 pm

AsgerJon wrote:...why can't I have a signature?

Unfortunately, many spammers use signatures for posting illicit links.
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Re: Product of linear equations

Postby Martingale on Sat Mar 12, 2011 9:33 pm

PM_Admin wrote:
AsgerJon wrote:...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. :wink: :D
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