Im not sure on the details, their CSR said that its to do with 'Telecom dropping their charges for the first time in years' (which is obviously a simplification of something more complicated going on). Im not sure where it applies, but from what I can tell by inputting a few addresses into the address checker on their website, it seems to apply in the main centres (Akl, wgtn, chch) but not in Kapiti (which normally has cheaper line rentals from Telecom to compete with the TCL HFC network despite not being a city). It doesnt appear to be related to LLU, altho i suspect it might not apply if you are on LLU gear.
To lock in the $9 saving - $42 rather than $51 per month for homeline - you need to sign a 12 month contract on your homeline.
Im only going on what i have discovered, nothing officially announced, but if you're a slingshot customer you might as well enter your address in their website address checker and give them a call. $9 is a lot to some people :)