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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 & 2 & 5 & 6 & 8 & 12 \\
\hline
Miles Driven & 425 & 967 & 1,253 & 1,253 & 2,648 \\
\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? Explain.

A. A scatter plot, because it would show the association, or relationship, between the two variables.

B. A scatter plot, because it would show how a variable changes over time between each individual data point.

C. A line graph, because it would show the association, or relationship, between the two variables.

D. A line graph, because it would show how a variable changes over time between each individual data point.



Answer :

GinnyAnswer
To determine the most appropriate graph to construct for the given data, let's analyze what we are trying to achieve with the graph.

The table provided shows the number of days and the corresponding total miles driven:

[tex]\[ \begin{tabular}{|c|c|c|c|c|c|} \hline Number of Days & 2 & 5 & 6 & 8 & 12 \\ \hline Miles Driven & 425 & 967 & 1,253 & 1,253 & 2,648 \\ \hline \end{tabular} \][/tex]

### Goal:
We want to observe how the miles driven change over a certain number of days. This implies that we are interested in seeing the progression or trend of the miles driven as time (days) passes.

### Types of Graphs:
1. Scatter Plot:
- A scatter plot shows individual data points and the relationship between two variables. It is useful for observing the correlation between variables but does not specifically highlight trends over time.

- Two reasons to use a scatter plot:
- To show the association or relationship between the two variables.
- To show how a variable changes over time between each individual data point.

2. Line Graph:
- A line graph connects data points with straight lines to help illustrate changes and trends over time. It is particularly effective for showing progression and trends between data points when the independent variable is a continuous variable like time.

- Two reasons to use a line graph:
- To show the association or relationship between the two variables.
- To show how a variable changes over time between each individual data point.

### Analysis:
Given that we are dealing with a sequence of data points over a period (days) and we want to observe how the miles driven change over this time, a line graph would be a suitable choice. This is because a line graph can effectively show trends and changes in the variable (miles driven) over the specified time period (days), connecting each day's data point to the next.

- Recommendation:
- A line graph, because it would show how a variable changes over time between each individual data point.

This option is optimal because it allows us to clearly see upward or downward trends in the number of miles driven over the various days, which is essential for understanding the progression of the road trip over time.

Thus, the most appropriate graph to use in this context is:
- A line graph, because it would show how a variable changes over time between each individual data point.

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