Question

How were northern lawmakers convinced to allow Missouri into the union as a slave state under the Missouri Compromise?

Answer 1

The northern lawmakers needed the state to join the union instead of the confederacy, because if they joined the confederacy, the Union would be weaker. They got the Missouri on their side by allowing it to hold slaves (but that could easily be overturned, so getting the state was more of a priority than having slavery or not) 

hope this helps