find the value of k such that the line containing point (2,k) is perpendicular to to the line y=2x-3 point (4,5).

Question

Please explain how you did it.

Answer 1

y=2x-3

the line perpendicular to this line has a slope that is the negative reciprocal of the slope 2, which is -1/2

y=mx+b

y=(-1/2)x+b

using point (4,5)

5=(-1/2)(4)+b

5=-2+b

b=7

y=(-1/2)x+7 is the equation of the perpendicular line

point (2,k)

k=(-1/2)(2)+7

k=-1+7

k=6