To determine the rate of change in the given description, we focus on the deduction of points related to how late the homework is turned in.
The homework is initially worth 100 points. If it is turned in late, there is a deduction of 5 points for each day the homework is late.
This means that for each day (let's call it \(d\)) that the homework is late, the total points deducted is represented as:
\[ \text{Points Deducted} = 5d \]
Therefore, the number of points remaining after \(d\) days can be expressed as:
\[ \text{Points Remaining} = 100 - 5d \]
The rate of change in this context is the amount of points deducted per one day of lateness, which is:
\[ \text{Rate of Change} = -5 \text{ points per day} \]
The negative sign indicates a decrease in points as the days increase. Thus, the rate of change is \(-5\) points per day.