Let there be two points P1(x1,y1) and P2(x2,y2)
The slope of the line between P1 and P2 is,
m = Δy/Δx, where Δy = y2 – y1 and Δx = x2 – x1
Using the points given in the question we have P1(x1,y1) = (a, f(a)) and P2(x2,y2) = (a+h, f(a+h))
Then,
m = Δy/Δx = (y2 – y1)/(x2 – x1)
where (y2 – y1) = f(a+h) - f(a), and (x2 – x1) = (a+h) – h = h
Therefore, the slope of the secant line is: Δy/Δx = [f(a+h) - f(a)]/h