The difference between y2 and y1 is called delta y and the symbol is ∆y
The difference between x2 and x1 is called delta x and the symbol is ∆x.
As the difference between x2 and x1(∆x) approaches 0 the slope approaches the instantaneous rate of change.
The denominatorcannot equal zero because in our system of mathmatics we cannot divide by zero!
The closer gets to zero the closer we get to the instaneous rate of change.
The mathematical limit is the ∆ y value.