Slope
Slope is the steepness of a line. A positive slope rises; a negative slope falls. Another term for slope is gradient.
For a straight line, the slope (m) is constant and represented by the difference in the vertical direction (y) divided by the difference in the horizontal direction (x):
The delta, Δ, represents the difference in values between any two points in the x or y direction for straight line. For a curve, the delta, Δ, represents the difference in values for two points in very close proximity to each other.
For a straight line, another way of representing the slope (m) is as follows:
where the two points are located at (x1, y1) and (x2, y2).
Introduction to derivative
If a function has value 
at 
and 
at 
with 
than the slope of the line joining 
to 
is,
.
The slope of the line that meets (is tangential to) at is the limit as 
tends to zero, or,
which is denoted 
, which is called the derivative of .
