Question

How does rate of change relate to slope?

Answer 1

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 $y=f(x+h)=3(x+h{)}^2$. (Just plug $x+h$ in for $x$). So, you get figure (ii).
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.
$y^{\prime }=f^{\prime }(x+h)=\left(\frac{d}{dx}\right)\left(3.\right(x{)}^2)=6x.1=6x$
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.