I did but I don't know if it is correct, could you give me the solution of the problem?
Are you sure that it is about refraction? Or is it about reflection??
I think you've to do this using the slope of the lines:
x+y=1 <=> y=1-x
so you know that the slope of this line is -1, and then you can use trigonometry: tg alfa = slope of the line <=> tg alfa = -1 <=> alfa = 135º
you said "it enters the opposite side after turning by 15degrees away from the line x+y=1", so you do: 135º+15º=150º
and then you have that the slope of the new line is tg 150º
and the equation of the new line is: y=tg 150ºx+1