SOLUTION: If f(x)=mx+b, and k≠0, find f(x+k)-f(x) /k

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Question 993320: If f(x)=mx+b, and k≠0, find f(x+k)-f(x) /k

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+mx+%2B+b.

f%28x%2Bk%29+=+m%28x%2Bk%29+%2B+b+=+mx+%2B+mk+%2B+b.


%28f%28x%2Bk%29+-+f%28x%29%29+%2F+k+=+%28mx+%2B+mk+%2B+b+-+%28mx+%2B+b%29%29+%2F+k which becomes:

%28f%28x%2Bk%29+-+f%28x%29%29+%2F+k+=+%28mx+%2B+mk+%2B+b+-+mx+-+b%29+%2F+k.

when you combine like terms in the numerator, the mx and the -mx cancel out and the b and the -b cancel out and you are left with:

%28f%28x%2Bk%29+-+f%28x%29%29+%2F+k+=+%28mk%29+%2F+k.

the k in the numerator and the denominator will cancel out and you will be left with:

%28f%28x%2Bk%29+-+f%28x%29%29+%2F+k+=+m.