Determine the value of k so that the line 2x pluse 5y equals 8 and the line k x minus 4 y equals 9 are perpendicular?

Answer 1

2x+5y=8

8-2x=5y

y=-0.4x+1.6

for y=mx+c, m is the gradient, -2/5. The perpendicular line will have a gradient of a negative reciprocal of the first, so 5/2 or 2.5.

kx-4y=9

kx-9=4y

y=(k/4)x-2.25

as such, k/4=2.5

k=10