The michaelis‑menten equation models the hyperbolic relationship between [s] and the initial reaction rate for an enzyme‑catalyzed, single‑substrate reaction e+s↽−−⇀es⟶e+pe+s↽−−⇀es⟶e+p . the model can be more readily understood when comparing three conditions: [s]< > km[s]> > km . match each statement with the condition that it describes. note that "rate" refers to initial velocity where steady state conditions are assumed. [total][total] refers to the total enzyme concentration and [efree][efree] refers to the concentration of free enzyme. [s]< > km[s]> > km not true for any of these conditions the rate is directly proportional to [s][s] . half of the active sites are filled with ss . almost all active sites are empty. [es][es] is much higher than [efree][efree] . reaction rate is independent of [s][s] . increasing [etotal][etotal] will increase kmkm .