  Recently a Lagrangian formulation for Rastall Gravity (RG) has been proposed
in the framework of f(R, T) gravity. In the present work we obtain Lagrangian
formulation for the standard Rastall theory assuming the matter content is a
perfect fluid with linear Equation of State (EoS). We therefore find a relation
between the coupling constant of the Lagrangian, the Rastall gravitational
coupling constant and the EoS parameter. We also propose a Lagrangian for the
Generalized Rastall Gravity (GRG). In this case the Rastall parameter which is
a constant is replaced by a variable one. More exactly, it appears as a
function of the Ricci scalar and the trace of the Energy Momentum Tensor (EMT).
In both mentioned models, the Lagrangians are constructed by a linear function
of R and T.
