The stack may be on the left, but the sink DRAIN line is on the right. The vent is the portion of the vertical riser above where the sinks connect. Whoever installed the drains was not a plumber. What you have to do, if anything, depends on what you mean by "drain slowly". Does one sink back up into the other when they are draining? Then the vertical line needs cleaning. Do both drain slowly but not back up" Then it could be a sink problem, not a drain stoppage. In either case, replacing the drain line is probably not the "cure".