In the xy-plane above, line k (not shown) is perpendicular to line l. What is the slope of line k?

Rationale

The slope of line k is -5.

Since line k is perpendicular to line l, which has a slope of 5, the slope of line k can be found using the negative reciprocal of the slope of line l. The negative reciprocal of 5 is -1/5, which can be expressed as -0.2.

A (5) YOUR ANSWER

This choice represents the slope of line l, not line k. Since line k is perpendicular to line l, it cannot have the same slope. Instead, the slope of line k must be the negative reciprocal of 5, making this option incorrect.

B (01-May) YOUR ANSWER

This choice is a nonsensical value in the context of slope and does not represent any valid numerical slope. Slopes are numerical values that describe the steepness of a line, and this option does not apply to the question at all.

C (-0.2) CORRECT

This choice accurately represents the slope of line k, which is the negative reciprocal of the slope of line l (5). Since the negative reciprocal of 5 is -1/5, this value is equivalent to -0.2, confirming that this is the correct answer.

D (-5) YOUR ANSWER

This choice suggests a slope of -5, which is incorrect. The negative reciprocal of 5 is -1/5, not -5. Thus, the slope of line k cannot be -5 as it would not satisfy the condition of being perpendicular to line l.

Conclusion

In summary, the slope of line k, being perpendicular to line l with a slope of 5, is determined to be -0.2. The negative reciprocal relationship between the slopes of two perpendicular lines is crucial in identifying their corresponding slopes. Thus, -0.2 is the only valid slope for line k among the provided choices.

In the xy-plane above, line k (not shown) is perpendicular to line l. What is the slope of line k?

The slope of line k is -5.

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