The diagram shows a triangle ABC where $A(-2, 3)$, $B(4, 5)$, and $C(6, 2)$ are vertices of $\triangle ABC$.
a. Find the slopes of sides $\overline{AB}$, $\overline{BC}$ and $\overline{AC}$
b. Find the angle between the sides $\overline{AB}$ and $\overline{BC}$ and the angle between $\overline{AB}$ and $\overline{AC}$
c. Find the equations of sides $\overline{AB}$ and $\overline{BC}$
d. Find the area of triangle $ABC$ and check if these three points are collinear.