Q:

Under what circumstances can a banker cut your line of credit?

I was once offered, and accepted, a line of credit for X. Apparently, I violated the terms (I believe that I made a late payment), and my line of credit was cut in half.
What is the legal doctrine or formula that allows a banker to do this?

A:

It's governed by your credit agreement or some similar document, which you surely signed as a condition of receiving credit.  There was almost certainly a clause that said the bank could reduce or revoke your credit line if you missed payments.

