Equilibrium thermodynamics should in principle only deal with equilibrium states. In an equilibrium state, the thermodynamic variables (for example $P,V,T$) are by definition constants: this is why the time variable $t$ never appears in thermodynamics.
However, when we use an equation of state $f(P,V,T)=0$ such as the ideal gas equation of state, $PV=nRT$, we expect that, if the transformation is slow enough, the equation should hold at every time during the transformation. For example, we expect that during a transformation at constant temperature of a rarefied gas, $P(V)$ should be an hyperbola.
We can state this formally by saying that during a quasistatic process we expect the relation
$$P(t) V(t) = n R T(t)$$
to hold $\forall t$. Of course, a quasistatic process is nothing but an idealization. Nevertheless, if the transformation is slow enough, we will observe that the equation of state is approximately verified.
For example, in numerical weather prediction, a set of six primitive equations in the variables $u,v,w,P,\rho,T$ is used ($u,v,w$ are the components of the velocity field vector, $P$ is the pressure, $\rho$ is the density and $T$ the temperature).
One of this equations is the equation of state
$$P = \rho R T$$
Without this equation, the system would not be solvable because we would have 6 unknowns and only 5 equations.
So we use the state equation in a situation in which the thermodynamic variables are clearly time-dependent. We do this because it is assumed that on atmospheric scales the change of the thermodynamic variables is slow enough for the equation of state to hold at every time.