Primer Line for Laundry Floor Drain

I am installing a floor drain in an upstairs laundry room and need to install a primer valve. The drain I am using has a trap primer port inlet on the side of the drain near the top. I am installing the primer valve under a nearby sink.

In order to run a 1/2" line to the drain, I will need to cross two floor joists. Does the 1/2" line need to slope downhill toward the drain? Or can it go down and then back up to meet the drain? My problem with trying to slope it is that the holes in the floor joists will be very close to the edge of the joist, much less than 2".

Thanks for any advice!

Should not go down then back up. It would work but then you would have water trapped in the discharge line from the trap primer all the time.
Does not have to be sloped, strait into your primmer tee is best.A 3/4 hole in the joist should be okay or a little larger than OD of the pipe.