Coupled rooms have a distinct sound energy decay behavior, which exhibits more than one decay time under certain conditions. The sound energy decay analysis in such scenarios requires decay models consisting of multiple exponentials with distinct decay rates and amplitudes. While multi-exponential decay analysis is commonly used in room acoustics, the spatial and directional sound energy decay variations in coupled rooms have received little attention. In this work, we introduce the common-slope model of late reverberation for coupled rooms. Common slopes are spatially and directionally invariant decay functions over time, whose amplitudes model all decay variations with respect to the source-receiver configuration. For example, in a scene consisting of two coupled rooms, it is possible to determine two common decay times that approximate the decay for all source-receiver configurations in the scene. Consequently, all spatial and directional decay variations are expressed via decay amplitudes only. We apply the common-slope analysis to measurements of room transitions between coupled rooms. Our analysis shows that the common-slope model approximates the measured sound energy decay with little error. The proposed common-slope model can be used for room acoustic analysis and the efficient synthesis of artificial late reverberation tails.