Question

How does the rate of change relate to the slope?

Answer 1

The slope of a line tells us how something changes over time. If we find the slope we can find the rate of change over that period. This can be applied to many real-life situations.

Complete step by step answer:
The 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. By finding the slope of the line, we would be calculating the rate of change.
${\text{Rate of change}} = \dfrac{{{\text{Change in y - values}}}}{{Change{\text{ in x - values}}}}$
We can't count the rise over the run lesson because our units on the x and y-axis are not the same. In most real-life problems, your units will not be the same on the x and y-axis. So, we need another method!
We will need to use a formula for finding slope given two points.
${\text{slope }} = \dfrac{{{\text{rise}}}}{{run}}$
$slope = \dfrac{{\Delta y}}{{\Delta x}} = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
Rate of Change Formula helps us to calculate the slope of a line if the coordinates of the points on the line are given.

Note: 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.