universe - If I were to point into the sky, how many galaxies would be in this line?

On average, you will point at one galaxy.

The argument goes as follows:

Looking at the spectrum of quasars, which are effectively point sources, and which lie at distances of the order of the size of the observable Universe, it turns out that typically, roughly one damped Lyman $alpha$ system (DLA) is detected. DLAs are huge reservoirs of neutral gas, which are early stages of galaxy formation.

At least in a handful of cases, the galaxy counterpart of the DLA has been confirmed. These observation are very challenging, since they are a faint sources at very small projected distances from the very bright quasar. Here's the setup:

So, accepting a DLA as a galaxy, I'd say that you will typically point at one galaxy.