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In this paper, we consider a comprehensive investigation of the cosmologicalmodel described by $f(R,T) = R + 2\lambda T$ (where $\lambda$ represents a freeparameter) in light of the most recent observational data. By constraining themodel using $Hubble$ and $Pantheon$ datasets, we determine its compatibilitywith the observed behavior of the Universe. For this purpose, we adopt aparametric form for the effective equation of state (EoS) parameter. Thisparametric form allows us to describe the evolution of the EoS parameter withrespect to redshift and investigate its behavior during different cosmicepochs. The analysis of the deceleration parameter reveals an acceleratingUniverse with a present value of $q_0=-0.64^{+0.03}_{-0.03}$, indicating thecurrent phase of accelerated expansion. The transition redshift is found to be$z_{tr}=0.53^{+0.04}_{-0.03}$, marking the epoch of transition fromdeceleration to acceleration. We also analyze the evolution of importantcosmological parameters including density parameter, pressure, effective EoS,and stability. These findings collectively demonstrate the viability of the$f(R,T)$ cosmological model as a robust candidate capable of engendering therequisite negative pressure, thereby efficiently propelling cosmic expansion.Moreover, the undertaken stability analysis underscores the model's stabilitywithin the broader cosmic landscape. By providing the best-fit values for thecoupling parameter $\lambda$, this approach motivates and encourages furtherexplorations into the extensive landscape of this model and its potentialapplications across diverse realms of cosmology and astronomy.

Constraining the $f(R,T) = R + 2\lambda T$ cosmological model using recent observational data