Slow light, i.e., the delay of an incident resonant pulse, can be observed in the throughput of an optical whisperinggallery microresonator. It can be produced by a single overcoupled whispering-gallery mode (WGM), or, more usefully, through induced transparency effects that are observed in the case of two coresonant WGMs with very different quality factors. There are several different methods for achieving induced transparency, two of which will be considered here. In addition, under the right conditions, light in a WGM can excite acoustic WGMs by forward Brillouin scattering. This nonlinear process due to electrostriction has a threshold, above which energy is transferred from the first optical WGM to the acoustic WGM and to a lower-frequency optical WGM. When one of the optical WGMs taking part in this optomechanical process is also involved in the production of slow light, the pulse delay can be affected. Analytical expressions for pulse delay in the three cases mentioned above are examined in terms of the WGM intracavity powers and it is shown that when the higher-frequency optical WGM is responsible for slow light, the pulse delay is reduced when the optomechanical process occurs. This conclusion is verified by a numerical model.