$k$ is an arbitrary constant. If you wanted to signify an addition of $+5$, then you could choose $k=5$ in the first form, but you could also choose $k=-5$ in the second. Both are equally acceptable from a mathematical standpoint. However, because of human biases, we often prefer the $+C$, or, in your case, $+k$ formulation just to cut down on the number of minus signs. We're a pretty positive species, on the whole.
ā DeepakMar 23 '23 at 00:10