  We study the sensitivities of the directed flow in Au+Au collisions on the
equation of state (EoS), employing the transport theoretical model JAM. The EoS
is modified by introducing a new collision term in order to control the
pressure of a system by appropriately selecting an azimuthal angle in two-body
collisions according to a given EoS. It is shown that this approach is an
efficient method to modify the EoS in a transport model. The beam energy
dependence of the directed flow of protons is examined with two different EoS,
a first-order phase transition and crossover. It is found that our approach
yields quite similar results as hydrodynamical predictions on the beam energy
dependence of the directed flow; Transport theory predicts a minimum in the
excitation function of the slope of proton directed flow and does indeed yield
negative directed flow, if the EoS with a first-order phase transition is
employed. Our result strongly suggests that the highest sensitivity for the
critical point can be seen in the beam energy range of $4.7\leq\srtNN\leq11.5$
GeV.
