Question 1179238
x  -  ky  -  17 = 0 makes an angle of 45 degrees counter-clockwise from the line x + 5y  -  4 = 0

one line is  5y=-x+4

y = -x/5   +4/5     slope = -(1/5)

Other line x-ky -17=0

ky=x-17

y= x/k =17/k

slopes are (-1/5) , (1/k)

 {{{tan(theta) =( m1-m2)/(1+m1m2)}}}

m1-m2= (1/k -(-1/5))

= (k+5)/5k------------N

1+m1m2 = 1+ (-1/5k) = (5k-1)/5k-----------D


N/D =1 = ((k+5)/5k) / ((5k-1)/5k))

1= k+5/ 5k-1

5k-1= k+5

4k =6
k=2/3