Final answer:
Broadened spectral lines in a galaxy's spectrum are indicative of its rotation due to the Doppler effect from the various speeds of its stars, which can be used to infer its mass and rotational velocity.
Step-by-step explanation:
When we observe that a spectral line of a galaxy is broadened, covering a range of wavelengths, we can conclude that the galaxy is rotating. This phenomenon, known as line broadening, occurs due to the Doppler shifts caused by the varying speeds of stars within the galaxy as they orbit its center. Some stars will be moving towards us, causing a blue shift, while others move away, leading to a red shift. These combined Doppler shifts from the multitude of stars result in the observed broadened spectral lines and can be used by astronomers to gather data about the rotational velocity and mass of a galaxy.