We investigate the propagation of neural activity along one-dimensional rat hippocampal cultures patterned in lines over Multi-Electrode Arrays. Activity occurs spontaneously or is stimulated by local electrical or chemical, with different resulting propagation velocities and firing rate amplitudes. A variability of an order of magnitude in velocity and amplitude is observed in spontaneous activity. A linear relation between velocity and amplitude is identified. We define a measure for neuron activation synchrony and find that it correlates with front velocity and is higher for electrically evoked fronts. We present a model that explains the linear relation between amplitude and velocity, which highlights the role of synchrony. The relation to current models for signal propagation in neural media is discussed.