1. A line-head control device that controls a line head, the line-head control device comprising: a calculation unit that divides image data into a plurality of areas in sub-scanning direction and calculates a printing percentage for each of the plurality of areas, wherein the printing percentage for each of the plurality of areas is a ratio of black data to total data in each of the areas respectively; an allocation unit that allocates a total correction amount, that is a correction amount for correcting magnification of the image data in the sub-scanning direction, to the plurality of areas according to the printing percentage for each of the plurality of areas calculated by the calculation unit; a control unit that changes an emission period of the light emitted from the line head so as to satisfy a partial correction amount that is an allocation of the total correction amount to each of the plurality of areas, exposes the image carrier to the light emitted from the line head with the changed light emission period, thereby causing a latent image to be formed on the image carrier based on the image data; and a storage unit that stores a printing percentage associated with a coefficient such that a value of the coefficient decreases stepwise as a value of the printing percentage increases, wherein the allocation unit allocates the total correction amount to each of the plurality of areas with ratios according to the coefficient associated with the printing percentage calculated by the calculation unit.