40. The scatterplot above shows a set of data values as well as a trend line for the data. Based on the trend line, which of the following best describes the relationship between x and y?
Answer: C
As x increases by 2, y tends to decrease by 1
The correct interpretation of the trend line indicates that for every increase of 2 units in x, there is a corresponding decrease of approximately 1 unit in y.
A) As x increases by 2, y tends to decrease by 6
This option incorrectly suggests a steep decline in y, which does not align with the trend line depicted in the scatterplot. The decrease of 6 units is not supported by the data presented.
B) As x increases by 2, y tends to decrease by 3
While this option indicates a decrease in y with an increase in x, the magnitude of decrease is inaccurate. The trend line shows that the decrease is not as significant as 3 units for every 2 units increase in x.
C) As x increases by 2, y tends to decrease by 1
This option accurately reflects the relationship observed in the trend line. It indicates a gradual decrease in y as x increases, matching the slope of the trend line closely.
D) As x increases by 2, y tends to remain constant
This option suggests that y does not change with an increase in x, which contradicts the trend line that clearly shows a decreasing relationship. The trend line depicts a downward slope rather than horizontal.
E) As x increases by 2, y tends to increase by 4
This option indicates an opposite relationship, suggesting that y increases as x increases. This is contrary to the trend line, which shows a decrease in y, not an increase.
Conclusion
The correct answer, which states that as x increases by 2, y tends to decrease by 1, is supported by the trend line in the scatterplot. The other options either exaggerate the decrease or incorrectly suggest no change or an increase, failing to accurately represent the observed data relationship.