I don’t really understand your question, you seem to be a bit confused about how this equation works. Either that, or you need to work on wording your questions more clearly. Assuming it’s the first one, here’s a brief explanation of what I think you’re talking about, but I’m going to try not to do it all for you, because this does sound like a homework question.
In the equation F=kx, k is the “spring constant”, so it doesn’t change no matter what, as long as you’re only talking about one spring. Therefore, the graph you describe, with k on one of the axes, would need to be talking about multiple springs. This is a weird graph, a graph with F and x on your axes would be much more common.
So, we’re making a graph that relates the spring constant k to the distance that a spring gets stretched. What’s missing from this graph? Force! Therefore, you must be talking about a graph of constant force. Your question now is: “if I exert the same force on a bunch of different springs with different stiffness, how far does each spring stretch?” Or, “if a spring is more stiff, does it stretch more or less than a less stiff spring with the same force applied to it?”
I hope this helps.
if it doesn’t help, it’s probably because you really want to be doing a force vs distance graph, not a spring constant vs distance graph