The quantities KM and Vmax are experimentally determined and different for each enzyme. Once you have an assay for enzyme activity, you can determine these parameters.
You can estimate KM and Vmax from the graph of initial velocity versus [S].
For this reason, the Lineweaver-Burke plot is used.
You can rearrange (6) into linear form: y=mx+b, if you let and .
Then (6) rearranges to:
If the data is plotted in this way, it looks like:
From this type of graph, it is easy to estimate KM and Vmax.