  In this manuscript, we consider the extension of the Hilbert-Einstein action
to analyze several interesting features of the theory. More specifically, the
Lagrangian $f(R)$ is replaced by $f(R, L_m)$ in action, where $R$ is the Ricci
scalar, and $L_m$ is the matter Lagrangian. We derive the motion equations for
a test particle in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) flat and
homogeneous spacetime. We also derive the energy conditions in this framework.
Then, we use the cosmographic parameter such as Hubble, deceleration, jerk, and
snap parameters to constraint the model parameters. As a result, we observe
that with the constraint range of model parameters our model shows the current
accelerated expansion of the universe.

General Relativity and Quantum Cosmology;High Energy Physics - Theory