  Using the theory of moduli of curves, we establish various slope inequalities
for general fibered surfaces. More precisely, we introduce the notion of
functorial divisors on Artin stacks and prove a theorem concerning their
effectiveness. Furthermore, we consider the moduli stack of reduced and local
complete intersection canonically polarized curves and prove that the closed
substack parametrizing non-stable curves has no divisorial components. Applying
the above theorems to some tautological divisors on various moduli stacks of
curves, we obtain several slope (in)equalities, e.g., a generalization of
Moriwaki's slope inequality, slope equalities of general fibered surfaces whose
fibers satisfy the Morsification conjecture. As applications, we provide a
positive answer to Reid's conjecture concerning algebraic Morsification of
non-hyperelliptic fibrations of genus $3$ and a positive partial answer to the
question posed by Lu and Tan regarding the Chern invariants of fiber germs.
