# Slope

### From Conservapedia

**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 (x_{1}, y_{1}) and (x_{2}, y_{2}).

### Introduction to derivative

If a function has value *f*(*x*) at *x* and *f*(*x* + *h*) at *x* + *h* with *h* > 0 than the slope of the line joining (*x*,*f*(*x*)) to (*x* + *h*,*f*(*x* + *h*)) is,

- .

The slope of the line that meets (is tangential to) *f*(*x*) at *x* is the limit as *h* tends to zero, or,

which is denoted *f*'(*x*), which is called the derivative of *f*(*x*).