The first observations of Io with the Space Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope (HST) showed that the brightest ultraviolet emissions come from localized regions near Io's equator, designated ``equatorial spots.'' This paper presents a detailed study of the location, shape, and brightness of the equatorial spots in near-monochromatic images obtained using STIS in the first-order long-slit spectroscopy mode. This study provides evidence that the equatorial emissions are linked to the interaction between the Jovian magnetosphere and Io's atmosphere. The morphology of the equatorial spots reported here provides additional information on the nature of this complex electrodynamic interaction. We find the following principal results: the locations of the equatorial spots are correlated with the Jovian magnetic field orientation at Io, but with a relation that is not 1:1; the equatorial spots are centered 10°-30° longitude downstream from Io's sub-Jovian longitude; the brightness of the emissions in this data set is correlated with Io's distance from the plasma torus centrifugal equator; and the anti-Jovian equatorial spots are ~20% brighter than the sub-Jovian equatorial spots.