Question

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

Answer 1

Line n passes through point K(5,-4) and is perpendicular to line m, as the slopes of lines n and m are negative reciprocals of each other.

Step-by-step explanation:

The equations of lines m and n are y=5/3x and y=-3/5x-1, respectively. To determine the relationship between these lines and point K(5,-4), we can substitute the x and y values of point K into each equation. For line m, substituting x = 5 gives us y = 5/3(5) = 25/3, which is not equal to -4, so point K does not lie on line m.

For line n, substituting x = 5 gives us y = -3/5(5) - 1 = -3 - 1 = -4, which matches the y-coordinate of point K. Hence, point K lies on line n.

To determine if the lines are perpendicular or parallel, we look at their slopes. Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. The slope of line m is 5/3 and the slope of line n is -3/5, which are negative reciprocals, confirming that line m is perpendicular to line n. Hence, option B is the correct answer: Line n passes through K and is perpendicular to line m.

Answer 2

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.