If the wire goes to the starter then the other end should either be on the alternator or the battery. Weird that it is black though.
any black wire must be first assumed as a ground, becareful, don't short out.
a slow starter would be; bad hot connection or wiring,
bad ground from trans ground post, possibly bad body ground,
bad batt or needs charge,
possibly needing a good hot connection from alt to batt, and alt grounding,
(bad starter),