Looking on the internet deeply has found these results:

drive on the highway is the most popular phrase on the web.

drive up the highway 11,570 results on the web	drive on the highway 12,080,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
And so the two of them prepared to drive up the coast. Right, and demand drives up the price. He was trying to drive up the price. We decided to drive up the coast. That drives up the cost of this robot. Drive up the main courtyard, unload there. We decided to drive up the coast. Right, drive up the ramps into the truck.	Road safety will not be impaired because drivers will not drive on the public highway and will drive for only a minimal number of hours per day. This is how we used to drive on the highways: At seventy I take it I took a little drive on the porcelain highway. I'm going to drive on the highway for the first time. Your brother let you drive on the highway? It's dangerous to drive slow on the highway, Mr. Abrams. five mph! He didn't drive on the highway.

drive up the highway

11,570 results on the web

drive on the highway

12,080,000 results on the web

More popular!

Road safety will not be impaired because drivers will not drive on the public highway and will drive for only a minimal number of hours per day.
This is how we used to drive on the highways: At seventy
I take it I took a little drive on the porcelain highway.
I'm going to drive on the highway for the first time.
Your brother let you drive on the highway?
It's dangerous to drive slow on the highway, Mr. Abrams.
five mph!
He didn't drive on the highway.