Sure! Let's analyze the given data step-by-step to understand the relationship between the number of days and the miles traveled.
The data is given in the form of a table:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
Days & 2 & 4 & 6 \\
\hline
Miles & 10 & 20 & 30 \\
\hline
\end{tabular}
\][/tex]
From this table, we can deduce the following:
1. Day 2: The number of miles traveled is 10.
2. Day 4: The number of miles traveled is 20.
3. Day 6: The number of miles traveled is 30.
Now, let's consider the relationship between the days and miles traveled. Notice that as the number of days increases, the miles traveled also increase. Specifically, for every increase in days, there seems to be a proportional increase in miles:
- From day 2 to day 4, the increase in days is \(4 - 2 = 2\) days. The corresponding increase in miles is \(20 - 10 = 10\) miles.
- From day 4 to day 6, the increase in days is \(6 - 4 = 2\) days. The corresponding increase in miles is \(30 - 20 = 10\) miles.
This suggests that for every 2 additional days, there are 10 additional miles traveled. Therefore, the rate of miles traveled per day can be calculated as follows:
[tex]\[
\text{Rate} = \frac{\text{Increase in miles}}{\text{Increase in days}} = \frac{10 \text{ miles}}{2 \text{ days}} = 5 \text{ miles/day}
\][/tex]
To check this constant rate, we can see if it applies across all data points given:
- From day 2 to day 4:
- Expected increase in miles = 2 days 5 miles/day = 10 miles
- Actual increase in miles = \(20 - 10 = 10\) miles
- Checkpoint passes.
- From day 4 to day 6:
- Expected increase in miles = 2 days 5 miles/day = 10 miles
- Actual increase in miles = \(30 - 20 = 10\) miles
- Checkpoint passes.
This confirms that the relationship holds true for the data provided. Therefore, the resulting set of values observed is:
- Days array: \([2, 4, 6]\)
- Miles array: \([10, 20, 30]\)
This matches the data given and adheres to the linear relationship deduced from the data.
