Slope

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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 .