[dtmredy1]

Water leaks in kitchen ceiling when it rains. There is an old gas vent pipe on the roof in about the same location as where it leaks into the ceiling

[KISS]

Pitch is the slope of the roof usually expressed as rise/run, but could be expressed as degrees.

The flashing or boot around the vent pipe may need to be replaced.

[KBC]

As a roofer I would try to explain to customers this,

A roof leaks where objects go through the shingles.The shingles don't leak(for 99% of cases)it's the pipes,the flashing,the valley's,etc. only where there are breaks in the shingles(or a VERY low pitched roof and the shingle wasn't properly installed/shingle wasn't appropriate for that application.. )

If the leak is near the pipe,it most likely IS from that pipe.

An improperly installed pipe boot could leak from day one of installing, or not for years.. even a properly installed boot can eventually leak, time and elements will break down just about anything.

Have a roofer or handyman who is experienced in pipe boot replacement,come and install a new one(the cost of the boot is less than $20.00 ANYWHERE I have even been) and to install(by an experienced person) isn't a difficult job.

I wonder why you asked about the pitch,though.. it there a real high pitch to your roof?Say a 12/12?(12" of rise to 12" of run)