This paper presents a novel mathematical model for visual search and selection time in linear menus. Assuming two visual search strategies, serial and directed, and a pointing sub-task, it captures the change of performance with five factors: 1) menu length, 2) menu organization, 3) target position , 4) absence/presence of target, and 5) practice. The novel aspect is that the model is expressed as probability density distribution of gaze, which allows for deriving total selection time. We present novel data that replicates and extends the Nielsen menu selection paradigm and uses eye-tracking and mouse tracking to confirm model predictions. The same parametrization yielded a high fit to both menu selection time and gaze distributions. The model has the potential to improve menu designs by helping designers identify more effective solutions without conducting empirical studies.