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[edit]

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 .