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In this paper, we have searched the existence of non-minimal matter-geometry coupling govern by power law in Bianchi I space-time. The energy and stability conditions are applied in the derived model to check the stability of the model and to obtain the certain range of values for the free parameters of the model that yield well behaved accelerating model of universe. We have also constructed a Lagrangian model which is based on f(R,T)=f1(R)+f2(R)f3(T) and it’s functional forms f1(R)=f2(R)=R and f3(T)=αT. We also examine the behaviour of physical parameters and validity of energy conditions as well as stability condition of derived model. Keywords: Bianchi I space-time, f(R,T) gravity, Matter-geometry coupling