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Linear focused grids are commonly used in general radiography and mammography to control scatter. In these applications, if lines would be visible when the grid was stationary, then the grid is moved during the x-ray exposure to blur out grid lines. Presented is a theoretical framework for estimating grid line artifact magnitude and evaluating artifact suppression techniques. The framework takes as parameters the grid pitch, septum thickness, and exposure time, and allows for a variation in grid velocity and in x-ray tube output during the exposure. Grid line artifacts are evaluated for a variety of conditions. These include a stationary grid, a grid moving at a constant velocity with no kV ripple, a grid moving at a constant velocity with large kV ripple, and a grid moving with decreasing velocity and no kV ripple. Also evaluated are grid line artifacts for a novel suppression technique in which the grid moves at a constant velocity and the x-ray exposure waveform is "feathered," i.e., when the x-ray exposure waveform has a soft start and stop. Of practical interest is that it is possible to effectively eliminate grid line artifacts when the grid moves only a short distance with an appropriately "feathered" exposure waveform. This capability permits one to design efficient and compact coarse strip density grid systems.