6. The graph of the inverse proportion function $y=\frac{k}{x}$ is an axially symmetric figure, one of its axes of symmetry is the graph of which of the following linear functions? ( ).
(A) $y=-k x$
(B) $y=|k| x$
(C) $y=\frac{-k}{|k|} x$
(D) $y=k x$
6. (C).

When $k>0$, the axis of symmetry is $y=-x$; when $k>0$, the axis of symmetry is $y=x$. Therefore, it is $y=-\frac{k}{|k|} x$.