Reaction constants in traditional Michaelis-Menten type enzyme kinetics are most often determined through a few linear plots. Such graphical plots sometimes provide reasonably good data. But, for a comparative survey, visual examinations are not enough. Instead, it is always advisable to go simultaneously for a few associated numerical tests. They can assess how far the measured values of the quantities sought are reliable, furnishing along with appropriate error estimates that can be checked against the corresponding nonlinear methods. Here, we explicitly deal with a few such situations to stress the importance of these tests with specific examples. Also, we advocate a new scheme to mainly highlight how cases may appear with negative reaction constants and explore the origin of such bizarre findings. This exercise, in turn, might even judge the quality of the input data set and modify it to suit the needs. Pilot calculations bring the worth to light. © 2017 Scientific Publishers. All rights reserved.