if the angle between the two lines 3x-5y-1=0 and Kx-y=3 is 45, then find the value of k

Answer 1

m1 = tanA = -3 /-5 = 0.6,
tanA = 0.6,
A = 31 deg.

B = 31 + 45 = 76 deg.

m2 = tanB,
m2 = tan76 = 4.0

m2 = -K / -1 = 4,
-K / -1 = 4,
Cross multiply:
-K = - 4,
K = 4.