I have been active on MSE for around 3-4 days. I have noticed the fact that people either ignore or downvote intuitive/graphical/visual analogies of a problem. However I feel that intuition is one of the most important things that one should walk hand-in-hand with while learning a subject like mathematics. I have always been posting graphical ways of thinking/visualising a given problem. I had to delete a correct answer due to too many downvotes, just because my answer was graphical and not mathematically-rigorous. And the accepted answer was the one which couldn't be solved by hand and used WolframAlpha to find the correct answer. Shall I stop giving intuitive answers?
I think graphics and visuals can be great for giving hints, intuition or suggesting what the solution should be, but they frequently fall short of giving a rigorous proof (for instance, the missing square puzzle). If the OP is looking for a rigorous proof, then a rigorous proof should be given - it can always be accompanied by a visual or graphic to give a better sense of what's going on, if that's appropriate to the question at hand.
You can also use the visual as a hint and put the full solution implied by the visual under a set of spoiler tags, like this answer, which was well-received after some initial downvotes for not being rigorous (for users not able to view vote counts, it is at +12/-5 at the time of writing, which is more upvotes than the currently accepted answer, at +10). This was discussed here on meta and here on chat in the past.