They are satellite terminal to transmit credit card data and receive authorization (or declination) from the credit card servicing provider. A private line? That doesn't seem an apt description. I was in a Wal-Mart store a year or so ago and no checks or credit cards could be accepted because "the satellite is down" (probably meant the satellite equipment was in trouble, either at that store or at the home terminal.)
(Checks are widely authorized now, too, by firms specializing in the service.)
Some chains also have high speed data links (not via satellite) for the same purpose.
Wes Leatherock snipped-for-privacy@aol.com snipped-for-privacy@yahoo.com