  In today's scenario, going beyond Einstein's theory of gravity leads us to
some more complete and modified gravity theories. One of them is the $f(R,T)$
gravity in which $ R $ is the Ricci scalar, and $ T $ is the trace of the
energy-momentum tensor. Using a well-motivated linear $f(R,T)$ gravity model
with a single parameter, we studied the strong energy condition (SEC), the weak
energy condition (WEC), the null energy condition (NEC), and the dominant
energy condition (DEC) under the simplest non-minimal matter geometry coupling
with a perfect fluid distribution. The model parameter is constrained by energy
conditions and a single parameter proposed equation of state (EoS), resulting
in the compatibility of the $f(R,T)$ models with the accelerated expansion of
the universe. It is seen that the EoS parameter illustrate the quintessence
phase in a dominated accelerated phase, pinpoint to the cosmological constant
yields as a prediction the phantom era. Also, the present values of the
cosmological constant and the acceleration of the universe are used to check
the viability of our linear $f(R,T)$ model of gravity. It is observed that the
positive behavior of DEC and WEC indicates the validation of the model. In
contrast, SEC is violating the condition resulting in the accelerated expansion
of the universe.
