Final answer:
The evidence for M82 X-1 being an intermediate-mass black hole is based on its X-ray variability, which indicates a compact mass indicative of a black hole, supported by the orbital characteristics of its companion star in a binary system.
Step-by-step explanation:
The best evidence for M82 X-1 being an intermediate-mass black hole comes from its X-ray variability. This variability suggests the presence of an accretion disk around a compact object, and the rapid changes in the X-ray emission indicate that this energetic radiation is produced in a very small region. Since the mass of the object can confine a significant amount of mass in such a small space, it is indicative of a black hole. Moreover, the characteristics of the binary system where M82 X-1 resides further support its classification as an intermediate-mass black hole, specifically through the motion and orbit of its companion star, which suggests the invisible companion's mass is substantial.