Question 523777
Kx-2y+13=0 
-2y=-kx-13=0
-2y/-2=(-kx-13)/-2
y=(k/2)x+13/2............(1)

Slope = k/2


9x-6y+11=0 
-6y=-9x-11
-6y/-6=(-9x-11)/-6
y=(9/6)x+11/6
y=(3/2)x+11/6
y=3x/2+11/6.............(3)

slope = 3/2
 

Since lines are perpendicular, multiplication of their slopes will result in (-1)

3/2 * k/2 = -1
3k/4=-1
3k=-4
k=-4/3

Value of K will be -4/3



Check
======

y=(k/2)x+13/2............(1)
Put the value of k in above equation
y=(-4/3)(1/2)x+13/2
y=(-2/3)x+13/2


 .........(4)
.............(3)

Graph
Red Line y=-2x/3+13/2
Green Line y=3x/2+11/6
{{{ graph( 500, 500, -10, 10, -10, 10, y=-2x/3+13/2,y=3x/2+11/6) }}}