I really don't know how to solve this. I'm having confusions. 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

Draw a rough figure.

The slope of L1 is 5/8 = tan of the angle L1 makes with the x axis.

The angle you want is that angle plus 60°, of which the tan is √3

The tan of the angle you want is obtained from the formula for the tan of the sum of 2 angles...

[(5/8)+√3]/[1-(5/8)√3].

Remember tan and slope mean essentially the same thing!