How to Find the Slope of the Line L2 (Analytic Geometry- Angle Between Two Lines)

Question

If L1 is the line through (-1, -3) and (7,2), find the slope of the line L2 so that the angle from L1 to L2 is 60°.

Answer 1

L1 has slope = (2+3)/(7+1) = 5/8

tan(5/8) = about 32 degrees with the x axis

L2's angle with the x axis would be 60+32 = 92 degrees, and virtually vertical in slope

tan92 = -28.56 = slope of L2

but L2's slope might also be tan(32-60) = tan-28 = tan332 = about -0.532