Enzyme Kinetics: A Modern Approach

If you do nonlinear analyses, you must also use residual graphs. They are much better than eyeballing whether a graph is linear or eyeballing if the data seem to fit a curve.
If you cannot do residual graphs, you should not use nonlinear analyses and stick with linear graphs, though even they are more dependable with the addition of a residual graph to check how well the data and equation fit. If you can do residuals, nonlinear analyses are faster, but not necessarily better in many cases. So, the reader should choose whether to use the author's method based on whether it is appropriate for their circumstances.