11. In the xy-plane above, line k (not shown) is perpendicular to line l. What is the slope of line k?
Answer: C
The slope of line k is -0.2.
Line k, being perpendicular to line l, has a slope that is the negative reciprocal of line l's slope. If line l has a slope of 5, then the slope of line k is calculated as -1/5, which simplifies to -0.2.
A) 5
This option represents a positive slope, which cannot be correct since line k is perpendicular to line l. If line l has a slope of 5, then line k must have a negative slope, making this option incorrect.
B) 01-May
This option is not relevant because it does not represent a numerical slope. Slopes are expressed as numerical values, making this choice invalid in the context of the question.
C) -0.2
This option is correct because if line l has a slope of 5, the slope of line k, being perpendicular, is indeed -1/5 or -0.2. This accurately reflects the relationship between the slopes of two perpendicular lines.
D) -5
This option suggests a slope that is not the negative reciprocal of 5. Instead, the correct relationship requires that line k's slope be -1/5, not -5. Therefore, this choice is incorrect.
Conclusion
The slope of line k is definitively -0.2, as it aligns with the geometric principle that states the slopes of two perpendicular lines are negative reciprocals of each other. All other options fail to meet this requirement, either suggesting incorrect slopes or being non-numeric.