We would most likely freeze to death. As the black hole crossed the asteroid belt we would be pulled away from the sun as it started to compete with the black hole's gravity. Depending how fast the black hole was moving we might die over a few months or we might freeze to death in a few days. Probably there are paths where the earth would briefly be pulled into an elliptical orbit, and then we would be burnt to a crisp as we circled back close to the sun.
