f ( R , T ) gravity is an extended theory of gravity in which the gravitational action contains general terms of both the Ricci scalar R and the trace of the energy-momentum tensor T . In this way, f ( R , T ) models are capable of describing a non-minimal coupling between geometry (through terms in R ) and matter (through terms in T ). In this article we construct a cosmological model from the simplest non-minimal matter–geometry coupling within the f ( R , T ) gravity formalism, by means of an effective energy-momentum tensor, given by the sum of the usual matter energy-momentum tensor with a dark energy contribution, with the latter coming from the matter–geometry coupling terms. We apply the energy conditions to our solutions in order to obtain a range of values for the free parameters of the model which yield a healthy and well-behaved scenario. For some values of the free parameters which are submissive to the energy conditions application, it is possible to predict a transition from a decelerated period of the expansion of the universe to a period of acceleration (dark energy era). We also propose further applications of this particular case of the f ( R , T ) formalism in order to check its reliability in other fields, rather than cosmology.