Question

A angle between line l and the line y-3=(-1/4)(x+2) measures 60 degrees. The line l contains the point (1,5). Find all possible equations of l.

Answer 1

\[y-3=-\frac{1}{4}(x+2)\]
\[y=-\frac{1}{4}x-\frac{1}{2}+3\]
\[y=-\frac{1}{4}x+\frac{5}{2}\]

Answer 2

One thing first.
The method I've been taught is to use
\[\tan \theta=\frac{ m1-m2 }{ 1+m1m2 }\]
where m1 and m2 are slopes of intersecting lines.

Answer 3

so I have
(Check if that's right, just in case.)