11. Line k has slope -2 and passes through point (3, -1). Quantity A: The x-intercept of line k, Quantity B: The y-intercept of line k
Answer: B
Quantity B is greater.
The y-intercept of line k is greater than the x-intercept. By calculating both intercepts, we can establish a clear comparison between the two quantities.
A) Quantity A is greater.
This option suggests that the x-intercept of line k is greater than the y-intercept. However, given the slope of -2 and the point (3, -1), the x-intercept can be calculated to be 1, while the y-intercept is -1. This proves that Quantity A is not greater.
B) Quantity B is greater.
This option is correct as the y-intercept, which is -1, is indeed greater than the x-intercept, which is 1. Thus, Quantity B is confirmed to be greater than Quantity A.
C) The two quantities are equal.
This option posits that both the x-intercept and y-intercept are the same. However, the calculations show that the x-intercept is 1 and the y-intercept is -1, indicating that they are not equal.
D) The relationship cannot be determined from the information given.
This option implies uncertainty regarding the comparison of the two quantities. However, since we can calculate both intercepts directly from the slope and point provided, the relationship can indeed be determined with certainty.
Conclusion
The correct answer is that Quantity B is greater, as the y-intercept (-1) is less than the x-intercept (1). All other options fail because they either misinterpret the relationship between the intercepts or incorrectly suggest that the relationship is indeterminate. Thus, the calculations clearly establish that Quantity B is definitively greater.