Full Text Article. Also available at: 10.1007/s10509-014-2131-4We find two new classes of exact solutions to the Einstein-Maxwell system of equations. The matter distribution satisfies a linear equation of state consistent with quark matter. The field equations are integrated by specifying forms for the measure of anisotropy and a gravitational potential which are physically reasonable. The first class has a constant potential and is regular in the stellar interior. It contains the familiar Einstein model as a limiting case and we can generate finite masses for the star. The second class has a variable potential and singularity at the center. A graphical analysis indicates that the matter variables are well behaved.