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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 .