Vacuum line question

Recently my A/C was only blowing throwing the defrost
vents. I found a vacuum hose that had broken off from this
thin vacuum line that comes out of the firewall on the
passenger side. This thin line is dry rotted and I want to
replace it however I am having a hard time finding out what
this line is called in order to purchase a replacement. I'm
also not sure exactly where this would attach to once
inside the firewall.