This paper is a generalization of earlier studies by Ferreira (1975) and Holbert and Broemeling (1977), who used improper prior distributions in order to make informal Bayesian inferences for the shift point and other parameters of a changing linear model. In this study, normal-gamma distributions are employed as prior distributions for the regression parameters of the model and, as a result, the posterior distribution of the regression parameters are mixtures oftdistributions, while a mixture of gamma distributions is the posterior distribution of the precision parameter.