Answer :
Before we can answer this question, it is important to understand the difference between the rate of change and the initial value.
The rate of change is the slope of a function. It describes the increase in y in response to an increase in x. In this problem, the y-axis represents the number of lawns mowed, and the x represents the months. So, the rate of change would be the number of lawns mowed per month.
The initial value in this problem describes how many lawns were mowed initially. It does not depend on x, which is what differentiates it from the rate of change. If we were thinking about a random function, it would be the y-intercept.
We are told that Homer mowed 5 lawns in the first month. This means that the initial value would be 5 lawns. We are also told that he increased the number of lawns he mowed by 2 each month. This means that each month, Homer mowed two more lawns than he did in the previous month. The rate of change is 2 lawns per month.
If we were to put these together, only the second choice accurately interprets the rate of change and the initial value. Initial value: 5 lawns, Rate of change: 2 lawns per month
