on thispicture the line touches the graph twice which meants it is a secant line. this changes which the coordinates are (x+h, f(x+h) )

with this we can derive the quotient formula and by that we plug in the secant coordinates to our slope formula which is y2-y1/x2-x1 when we plug everything in all we need to do is cancel the x's and end up with the formula which is (f(x+h)-f(x)) /h