  The observational evidence regarding the present cosmological aspects tells
us about the presence of very little anisotropy in the universe on a large
scale. Here, in this paper, we attempt to study locally rotationally symmetric
(LRS) homogeneous Bianchi-I spacetime with the isotropic matter distribution.
This is done within the framework of $f(\mathcal{R},\mathscr{L}_m)$ gravity.
Particularly, we consider a non-linear $f(\mathcal{R},\mathscr{L}_m)$ model,
$f(\mathcal{R},\mathscr{L}_m)=\dfrac{1}{2}\mathcal{R}+\mathscr{L}_m^{\,{\alpha}}$.
Furthermore, $\omega$, the equation of state parameter, which is vital stuff in
determining the present phase of the universe is constrained. To constrain the
model parameters and the equation of state parameter, we use 57 Hubble data
points and 1048 Pantheon supernovae type Ia data sample. And, for our
statistical analysis, we use Markoc Chain Monte Carlo (MCMC) simulation.
Moreover, with the help of obtained values of parameters, we measure the
anisotropy parameter for our model.
