# How does rate of change relate to slope?

Apr 15, 2018

As below.

#### Explanation:

Slope is the ratio of the vertical and horizontal changes between two points on a surface or a line.
The vertical change between two points is called the rise, and the horizontal change is called the run.
The slope equals the rise divided by the run: .
This simple equation is called the slope formula.

If $y = f \left(x + h\right) = 3 {\left(x + h\right)}^{2}$, (Just plug x + h in for x). So, you get this:

The instantaneous rate of change, or derivative, can be written as dy/dx, and it is a function that tells you the instantaneous rate of change at any point.

$y ' = f ' \left(x + h\right) = \left(\frac{d}{\mathrm{dx}}\right) \left(3 \cdot {\left(x\right)}^{2}\right) = 6 x \cdot 1 = 6 x$

. For example, if x = 1, then the instantaneous rate of change is 6.

Rate of Change Formula helps us to calculate the slope of a line if the coordinates of the points on the line are given. ... If coordinates of any two points of a line are given, then the rate of change is the ratio of the change in the y-coordinates to the change in the x-coordinates.

Hope this helps.