Question 829839
Find y for what?  The intersection of the defined line?  The angle is not needed for that.


First line, slope (-7-10)/(4-(-1))=-17/5
b=y-mx
b=-7-(-17/5)4=-7+68/5=6.6
y=-(17/5)x-3.6
Solve for x
5y=-17x-18
5y+18=-17x
x=-(5y+18)/17


Second line, slope (-9-2)/(-1-4)=11/5
b=y-mx
b=2-(11/5)4=2-44/5=-6.8
y=(11/5)x-6.8
Solve for x
y+6.8=(11/5)x
x=(5/11)(y+6.8)


The x expressions must equal at the intersection.
-(5y+18)/17=5(y+6.8)/11
-11(5y+18)=15*5(y+6.8)
-55y-18*11=5*15y+5*15*6.8
-55y-5*15y=15*5*6.8+18*11
y(55+5*15)=-(5*15*6.8+18*11)
130y=-708
y=-(708)/130
y=-5.446


Was that what you wanted?