find the value of n so that the line perpendicular to the line with the equation -2y+4=6x+8 passes through the points at (n,-4) and (2,-8).

Question

find the value of n so that the line perpendicular to the line with the equation -2y+4=6x+8 passes through the points at (n,-4) and (2,-8).

Answer 1

-2y + 4 = 6x + 8

-2y = 6x + 4

y = -3x - 2

So, the slope of the given line is -3.

Slope of perpendicular line = (-8-(-4)) / (2 - n) = 4 / (n-2)

So, 4 / (n-2) = 1/3 (Since the slopes of perpendicular lines are negative reciprocals of each other)

Cross multiplying, we have n - 2 = 12. So, n = 14.