  We compute the component field 4-dimensional N=1 supergravity Lagrangian that
is obtained from a superfield Lagrangian in the U(1)_K formalism with a linear
dilaton multiplet. All fermionic terms are presented. In a variety of important
ways, our results generalize those that have been reported previously, and are
flexible enough to accomodate many situations of phenomenological interest in
string-inspired effective supergravity, especially models based on orbifold
compactifications of the weakly-coupled heterotic string. We provide for an
effective theory of hidden gaugino and matter condensation. We include
supersymmetric Green-Schwarz counterterms associated with the cancellation of
U(1) and modular duality anomalies; the modular duality counterterm is of a
rather general form. Our assumed form for the dilaton Kahler potential is quite
general and can accomodate Kahler stabilization methods. We note possible
applications of our results. We also discuss the usefulness of the linear
dilaton formulation as a complement to the chiral dilaton approach.
