SOLUTION: find the slope of the line joining the points whose coordinates are given. (a,b), (b,a)

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Question 336497: find the slope of the line joining the points whose coordinates are given. (a,b), (b,a)
Answer by jim_thompson5910(28476) About Me  (Show Source):
You can put this solution on YOUR website!
Note: is the first point . So this means that x%5B1%5D=a and y%5B1%5D=b.
Also, is the second point . So this means that x%5B2%5D=b and y%5B2%5D=a.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28a-b%29%2F%28b-a%29 Plug in y%5B2%5D=a, y%5B1%5D=b, x%5B2%5D=b, and x%5B1%5D=a


m=%28a-b%29%2F%28-1%28-b%2Ba%29%29 Factor out a -1 from the denominator.


m=-%28a-b%29%2F%28a-b%29 Rearrange the terms.


m=-cross%28%28a-b%29%29%2Fcross%28%28a-b%29%29 Cancel out the common terms.


m=-1 Simplify


So the slope of the line through the points (a,b) and (b,a) is m=-1. This is true regardless of the values of 'a' and 'b' as long as a%3C%3Eb


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Jim