A family went on a cross-country road trip for their summer vacation. The following table shows the number of days and the total amount of miles their car had driven.

\begin{tabular}{|c|c|c|c|c|c|}
\hline Number of Days & 1 & 3 & 7 & 10 & 15 \\
\hline Miles Driven & 380 & 984 & 1,986 & 2,251 & 3,623 \\
\hline
\end{tabular}

Which of the following graphs is most appropriate to construct for the data given in the table to observe how the miles change over a certain number of days?

A. A scatter plot, because it would show how a variable changes over time between each individual data point
B. A scatter plot, because it would show the association, or relationship, between the two variables
C. A line graph, because it would show how a variable changes over time between each individual data point
D. A line graph, because it would show the association, or relationship, between the two variables



Answer :

To determine which type of graph is most appropriate for the given data, let’s analyze the requirements and characteristics of the data:

### Data Analysis:
The data table presents two variables:
1. Number of Days
2. Miles Driven

The goal is to select a graph that can accurately depict how the number of miles driven changes over the days.

### Characteristics of Each Graph Type:
1. Scatter Plot: This graph plots individual data points but does not connect them. It is useful for showing relationships or correlations between two variables, but it doesn't necessarily highlight trends over time as clearly as a line graph.

2. Line Graph: This graph connects data points with lines, making it effective at showing trends over periods. When the goal is to observe changes over time, a line graph is particularly useful because it visually emphasizes the progression and trend.

### Given Data in Context:
- The number of days is a continuous measure of time.
- Miles driven varies over these days and needs to reflect change over this period.

### Reason for Choice:
In this scenario, we are interested in observing how the miles driven change over a range of days. A line graph is ideal here as it can clearly show the continuous change from one point to another over time. This graph type connects the data points and makes it easier to see the trend in miles driven as days progress.

### Answer:
The most appropriate graph for this data is:
- A line graph, because it would show how a variable changes over time between each individual data point.

This type of graph effectively demonstrates the relationship between the number of days and miles driven over those days, making it easier to observe the trend and any patterns in the data.

### Conclusion:
Therefore, the appropriate graph to construct for the data given in the table to observe how the miles change over a certain number of days is:
A line graph, because it would show how a variable changes over time between each individual data point.

Thus, the correct answer to this question is:
A line graph, because it would show how a variable changes over time between each individual data point.