To determine which scatter plot best represents the data, let's consider the key points about a good scatter plot:
1. Reasonable Scale on Both Axes: The scales on the axes should be such that the spread of data points uses the available space effectively without being too cramped or too spread out.
2. Explanatory Variable on the X-Axis: In this context, the distance (which is the explanatory variable) should be plotted on the x-axis and the time (which is the response variable) on the y-axis.
Let's analyze the table data:
[tex]\[
\begin{array}{lrrrrrrr}
\hline
\text{Distance (km)} & 1 & 2 & 3 & 4 & 5 & 6 \\
\text{Time (minutes)} & 5.1 & 11.8 & 17.7 & 25.2 & 33.0 & 41.9 \\
\end{array}
\][/tex]
Now, review each graph:
Graph A:
- Scale might be spread too much, which could make data points appear far apart.
- Check if the explanatory variable is on the x-axis.
Graph B:
- Axis scales could be more reasonable compared to Graph A, using space more effectively.
- Ensure the explanatory variable is on the x-axis.
Graph C:
- Sometimes has a cramped scale that could squash the data points.
- Verify if it maintains the explanatory variable on the x-axis.
Graph D:
- Plot may effectively use the space and appropriately scale both axes.
- Ensure the distance is correctly on the x-axis.
Given the information from the table and the correct interpretation principles, Graph B likely provides the best representation:
- It uses a reasonable scale on both axes, distributing the data points evenly and effectively.
- It correctly places the explanatory variable, distance, on the x-axis, and the response variable, time, on the y-axis.
Thus, the best choice is:
(B) Graph B
