Answer:
-600
Step-by-step explanation:
The rate of change of a function f(x) in a certain interval
is the ratio between the change of the function and the change in the value of x:
![r=\frac{f(x_2)-f(x_1)}{x_2-x_1}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bf%28x_2%29-f%28x_1%29%7D%7Bx_2-x_1%7D)
The rate of change of a function tells how much the value of the function is changing per change in unit of x: therefore, for a linear function it corresponds to the slope of the line.
In this problem, the function f(x) is equal to the value of the business machine in dollars, while the variable x represents the number of years.
Here we are told that the machine was purchased for
![q=\$4500](https://tex.z-dn.net/?f=q%3D%5C%244500)
while its value decreases by $600 each year, so
![m=-600\$](https://tex.z-dn.net/?f=m%3D-600%5C%24)
This means that the linear function that represents the value of the machine after x years is:
![y=4500-600x](https://tex.z-dn.net/?f=y%3D4500-600x)
Therefore, the rate of change of the function is -600.