Explain the slope-deflection equations and their application.

Slope-deflection equations express end moments of a beam member in terms of rotations and settlements at ends: Mab = 2EI/L(2θa + θb - 3ψ) + FEMab, where θ are rotations, ψ is chord rotation due to settlement, and FEM is fixed-end moment. These equations are applied at each joint where sum of moments must equal zero, creating simultaneous equations to solve for unknown rotations. They're exact for members with constant EI.