Find the value of b if the lines 2x - y +1 =0 and bx -7y +5 = 0 make an angle of 45° at their intersection.

Answer 1

L1: y = 2x+1
L2: y = (bx+5)/7

assuming that b/7 > 2, we have, using
tan(A-B) = (tanA-tanB)/(1+tanAtanB)

we want to find b such that

(b/7 - 2)/(1+(b/7)(2)) = 1
b = -21, and we have

L2: -3x + 5/7
or any parallel line with slope -3.

check:
arctan(-3) = 108.43°
arctan(2) = 63.43°

difference is 45°