Although the present universe is believed to be homogeneous and isotropic on large scales, there is some evidence of some anisotropy at early times, Hence, there is interest in the Bianchi models, which are homogeneous, but anisotropic. In this presentation, the Bianchi type–I space-time in the framework of the f(R,T) modified theory of gravity has been investigated for the specific choice of f(R,T) = R + 2f(T), where f(T) = - mT, m = constant. The solution of the modified gravity field equations has been generated by assuming that the deceleration parameter q is a simple linear function of the Hubble parameter H, i.e., q = b - d/H, (where b and d are constants, and d > 0 ) which yields the scale factor a = k[exp(dt) - 1]^1/(1+b) (where k is a constant). The model exhibits deceleration at early times, and is currently accelerating. It is also seen that the model approaches isotropy at late times. Expressions for the Hubble parameter in terms of red-shift, luminosity distance, and state-finder parameter are derived and their significance is described in detail. The physical properties of the cosmological model are also discussed. An interesting feature of the model is that it has a dynamic cosmological parameter, which is large during the early universe, decreases with time, and approaches a constant at late times. This may help in solving the cosmological constant problem.