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 -1/15.

Since line k is perpendicular to line l, its slope is the negative reciprocal of the slope of line l. Given that the slope of line l is 15, the slope of line k is calculated as -1/15, indicating that for every 15 units the line rises, it falls 1 unit, establishing a steep negative slope.

A (5) YOUR ANSWER

A slope of 5 indicates a line that rises 5 units for every 1 unit it moves horizontally. This value does not represent a negative reciprocal of any slope associated with line l (which has a slope of 15), and hence cannot be the slope of line k.

B (15) CORRECT

A slope of 15 represents the slope of line l, not line k. Since line k is perpendicular to line l, it cannot have the same slope; rather, it must be the negative reciprocal of 15, which is -1/15.

C (-16) YOUR ANSWER

A slope of -16 indicates a very steep decline, which is not the negative reciprocal of 15. This value does not satisfy the condition of being perpendicular to line l, as the correct slope for line k must be much less steep, specifically -1/15.

D (-5) YOUR ANSWER

A slope of -5 indicates that for every 1 unit the line moves horizontally, it falls 5 units. This slope is not the negative reciprocal of line l's slope of 15, and thus does not conform to the requirement for perpendicular lines.

Conclusion

Perpendicular lines in a plane have slopes that are negative reciprocals of one another. For line l with a slope of 15, the corresponding slope of line k, which is perpendicular to line l, is -1/15, confirming that the only correct option aligns with this mathematical principle.

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 -1/15.

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