Question 1176801
<pre>
{{{ (f(x+h)-f(x))/h}}}

First find f(x+h) by substituting (x+h) for x

{{{f(x+h) = a(x+h)+b}}}

Then substitute in the expression at the top:

{{{ ((a(x+h)^""+b^"")-(ax+b^"")^"")/h^""}}}

Now simplify. Remove the inner parentheses:

{{{ ( (ax+ah+b^"")-(ax+b^"")^"")/h^""}}}

Remove the other parentheses:

{{{ (ax+ah+b^""-ax-b^"")/h^""}}}

{{{ (cross(ax)+ah+cross(b)^""-cross(ax)-cross(b)^"")/h^""}}}

{{{ah^""/h""}}}

{{{a*cross(h)^""/cross(h)""}}}

{{{a}}}   <-- answer

Notice that the slope of f(x) = ax+b is a [Thinking of y=mx+b]

This demonstrates that the difference quotient of a linear function
is always equal to the slope of the line. [I just threw that in.]

Edwin</pre>