Question 8

As x increases by 8, y tends to decrease by 6.

The scatterplot indicates a negative relationship between x and y, where an increase in x corresponds to a decrease in y. Specifically, the trend line suggests that for every increase of 8 units in x, y decreases by approximately 6 units.

A) As x increases by 8, y tends to decrease by 6.

This option accurately reflects the relationship shown in the scatterplot. The trend line indicates a clear downward slope, confirming that y decreases as x increases, specifically by 6 units for every 8 unit increase in x.

B) As x increases by 8, y tends to decrease by 4.

This option is incorrect because the data supports a decrease of 6 units in y, not 4. The trend line's slope is steeper than what would suggest a decrease of only 4 units for an 8 unit increase in x.

C) As x increases by 8, y tends to decrease by 2.

This option misrepresents the data as it implies a much shallower negative slope than what is depicted in the scatterplot. The trend line clearly shows a more significant decrease in y than just 2 units for an increase of 8 units in x.

D) As x increases by 8, y tends to remain constant.

This option is incorrect as it contradicts the visible downward trend in the scatterplot. The trend line indicates that y does not remain constant but rather decreases as x increases.

E) As x increases by 8, y tends to increase by 2.

This option is also incorrect as it indicates a positive relationship between x and y, which is not supported by the trend line. The scatterplot shows a negative correlation, where y decreases rather than increases with an increase in x.

Conclusion

Option A is definitively correct as it accurately describes the negative relationship between x and y illustrated in the scatterplot. All other options fail to capture the true nature of the relationship, either suggesting a lesser decrease, an incorrect constancy, or a reversal of the trend.