To determine the initial value (y-intercept) in the context of this table, we need to analyze the relationship between the number of days the book is overdue and the corresponding fine amount.
From the values given:
- For 2 days, the fine is 30 cents.
- For 3 days, the fine is 45 cents.
- For 4 days, the fine is 60 cents.
It appears that the fine increases based on the number of overdue days. Since we need to find the initial fine amount (when the number of overdue days is zero), we can extrapolate from the data.
To find the initial fine amount, we can analyze the trend in the fines:
- From 2 to 3 days: 30 cents to 45 cents (increase of 15 cents)
- From 3 to 4 days: 45 cents to 60 cents (increase of 15 cents)
This indicates a linear relationship, and suggests that for each additional day overdue, the fine increases by 15 cents.
To find the initial fine amount (at 0 days), we can set up the equation based on the linear relationship. The fines at 2 days (30 cents) can be represented in the linear form as:
Fine = Rate * Days + Initial fine
Using the known points, we can first find the rate. If we take the increase as 15 cents per day and denote it as 'r':
At 2 days: \[ 30 = 15 \cdot 2 + Initial\ value\]
Solving for the Initial value, we subtract 30 cents from 30:
\[ Initial\ value = 30 - 30 = 0\]
So, the initial value (fine owed when the book is 0 days overdue) is 0 cents.
In conclusion, the initial fine amount is 0 cents.