Sphingosine-1-phosphate (S1P) is important for cell survival. The synthesis of S1P from sphingosine and ATP is catalyzed by the enzyme sphingosine kinase. An understanding of the kinetics of the sphingosine kinase reaction may be important in the development of drugs to treat cancer. The velocity of the sphingosine kinase reaction was measured in the presence and absence of threo-sphingosine, a stereoisomer of sphingosine that inhibits the enzyme. The results are shown below.

Construct a Lineweaver–Burk plot to answer the following questions:
(a) What are the apparent KM and Vmax values in the presence and absence of the inhibitor?
(b) What kind of an inhibitor is threo-sphingosine? Explain.

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[Sphingosine] (m) 2.5 3.5 5 10 20 50 V. (mg. min-) (no inhibitor) 32.3 40 50.8 72 87.7 115.4 v. (mg. min-) threo-sphingosine) (with 8.5 11.5 14.6 25.4 43.9 70.8