Two distinct lines are drawn such that the first line passes through point \(P\) on the positive \(y\)-axis and the second line passes through point \(Q\) on the positive \(x\)-axis. Line segment \(PQ\) is perpendicular to both lines.
If the line through \(P\) has equation \(y=mx+k\), then determine the \(y\)-intercept of the line through \(Q\) in terms of \(m\) and \(k\).
Suggestion: If you are finding the general problem difficult to start, consider first solving a problem with a specific example for the line through \(P\), like \(y=4x+3\), and then attempt the more general problem.