The rate of change can be thought of as the slope of the line that passes through all the points, when plotted on a the x-y plant.
Alternatively, the rate of change can be thought of as the rate at which the output is changing as compared to the change in input.
According to the second explanation, the rate of change can be written as:
![\text{rate of change=}\frac{change\text{ in output}}{\text{change in input}}]()
Now, let us select to inputs and their corresponding outputs.
Thus:
for input 0, we have output 2
for input 3, we have output -1
Therefore:
![\text{change in input = 3-0=3}]()
and:
![\text{change in output= -1-2 = -3}]()
The rate of change is thus:
![\begin{gathered} \text{rate of change=}\frac{change\text{ in output}}{\text{change in input}} \\ \Rightarrow\text{rate of change=}(-3)/(3)=-1 \\ \Rightarrow\text{rate of change=}-1 \end{gathered}]()
Therefore, the rate of change is -1