Different graphical plots involving the catalytic rate and the (initial) substrate concentration exist in the enzyme kinetics literature to estimate the reaction constants. But, none of these standard plots can unambiguously distinguish between the two important mechanisms of rate enhancement: positive cooperativity among the active sites of an oligomeric enzyme and auto catalysis of the intermediate complex of an enzyme with a single active site. In the simplest situation of a direct autocatalysis, at least, we have achieved this distinction here by providing a nice linear plot for the latter. Importantly, to accomplish this task, no extra information other than the steady-state rate as a function of substrate concentration is required. In case of regression of the rate, a similar scheme can also distinguish negative cooperativity from autoinhibition.