This paper examined observed score linear equating in two different data collection designs, the equivalent groups design and the nonequivalent groups design, when information from covariates (i.e., background variables correlated with the test scores) was included. The main purpose of the study was to examine the effect (i.e., bias, variance, and mean squared error) on the estimators of including this additional information. A model for observed score linear equating with covariates first was suggested. As a second step, the model was used in a simulation study to show that the use of covariates such as gender and education can increase the accuracy of an equating by reducing the mean squared error of the estimators. Finally, data from two administrations of the Swedish Scholastic Assessment Test were used to illustrate the use of the model.