The coordinates of points A and B are \((-3k - 1, k + 3)\) and \((k + 3, 3k + 5)\) respectively, where \(k\) is a constant \((k \neq -1)\).

1. Find and simplify the gradient of \(AB\), showing that it is independent of \(k\).
2. Find and simplify the equation of the perpendicular bisector of \(AB\).