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?