Problem with slopes and angles?

Question

I tried to solve this one many times but I can't get to the correct answer. Any suggestions on how to solve this one?

The angle that is made by the lines (-4, 5) (3, y) and by the line (-2, 4) (9, 1) is 135°. Find y.

The answer should be y = 9. I'd really appreciate an explanation, because I keep getting y = 6193/197

Answer 1

Find the slope of the line thru (-4, 5) and (3, y).
m = ∆y/∆x = (y - 5)/(3 + 4) = (y - 5)/7
tanα = m = (y - 5)/7

Find the slope of the line thru (-2, 4) and (9, 1).
m = ∆y/∆x = (1 - 4)/(9 + 2) = -3/11
tanβ = m = -3/11

135° = β - α
tan(135°) = tan(β - α) = (tanβ - tanα) / [1 + (tanα)(tanβ)]
(-3/11 - (y - 5)/7) / [1 + (-3/11)((y - 5)/7)] = -1
(-21 - 11(y - 5) / [77 - 3(y - 5)] = -1
(-21 - 11y + 55) / (77 - 3y + 15) = -1
(34 - 11y) / (92 - 3y) = -1
34 - 11y = -92 + 3y
126 = 14y
9 = y