23. In the xy-plane above, line k (not shown) is perpendicular to line l. What is the slope of line k?
Answer: B
The slope of line k is 15.
Line k, being perpendicular to line l, has a slope that is the negative reciprocal of the slope of line l. Since the slope of line l is 1/15, the slope of line k would be 15.
A) 5
This option is incorrect because a slope of 5 does not represent the negative reciprocal of a slope that would yield a perpendicular line with a slope of 1/15. The relationship between perpendicular slopes does not support this value.
B) 15
This option is correct because if line l has a slope of 1/15, then the slope of line k, which is perpendicular to line l, must be the negative reciprocal. The negative reciprocal of 1/15 is indeed 15.
C) -16
This option is incorrect because -16 does not represent the negative reciprocal of the slope of line l. The relationship between perpendicular lines does not yield this value when starting from a slope of 1/15.
D) -5
This option is incorrect as well because -5 is not the negative reciprocal of 1/15. The correct negative reciprocal that would ensure perpendicularity is 15, not -5.
Conclusion
The correct answer is 15 because it accurately reflects the negative reciprocal of the slope of line l, which is necessary for determining the slope of a line that is perpendicular to it. All other options fail to meet the criteria for perpendicular slopes based on the given information.