the derivative is the slop of the straight line of the curve. We suppose that in axis X is time and in axis Y is position, te slop has unit of velocity.
In your example -9.8t+16, is the slop in any instant of time, I mean, if you want find the straight line of the curve equation in t=2s, only you subtitute. Then in t=2s our original function we give a position, now you have a point and the slope, whit this you can find the straight line of the curve equation in t=2s
P.D: if you understan spanish I can explain this better