The equation of line m is y=5/3x. the equation of line n is y=-3/5x-1. which best describes the relationship between line m, line n, and point k(5,-4)

a. line m passes through k and is perpendicular to line n.
b. line n passes through k and is perpendicular to line m.
c. line m passes through k and is parallel to line n
d. line n passes through k and is parallel to line m

B

Step-by-step explanation:

Parallel lines have the same slope while perpendicular lines have slopes which are negative reciprocals.

Here the slope of line m is 5/3.

Here the slope of line n is -3/5.

These lines are perpendicular.

Line n crosses through point k and can be shown through substitution. Substitute (5,-4) into line n.

y = -3/5 x - 1

-4 = -3/5(5) - 1

-4 = -15/5 - 1

-4 = -3 - 1

-4 = -4

The solution is B where n passes through K and the lines are perpendicular.