Question

Let f(x)=8x+7. Then the expression [f(x+h)-f(x)]/h can be written in the form of Ah+Bx+C. A, B, and C are constant and it is possible for one or more to be 0.

Find A, B, C.

Answer 1

this expression is the slope of the line connecting points (x,f(x)) and (x+h,f(x+h)), since slope=(y2-y1)/(x2-x1). both points lie on the line y=f(x); the slope of this line is 8; thus A=0, B=8, C=0.