Larry N. said:
I see two posts above saying that Interstates are not very steep. But I-70 west of Denver has a number of 5% and 6% grades, which I'd consider fairly steep, especially since a few are several miles long, and they have runaway truck ramps periodically. In fact I-70 was closed the other day for over 24 hours, due to a semi that plowed into some traffic that was slowed/stopped for an accident ahead. Video showed a huge fireball, and 28 vehicle were involved, four people killed. The driver says his brakes failed -- that's normally what can happen when brakes are improperly used on steep descents.
For the OP, the big principal involved is to not ride the brakes -- you MUST gear down. On the steeper sections that will often, depending on your vehicle, mean being slow enough to be in a gear low enough that you don't need brakes very much, say briefly every minute or two. An oft-quoted rule is to go down hills in the same gear you would need to go up that hill, but I'd add the caveat that if you're needing brakes every few seconds or if you need to apply them for more than 5-10 seconds every couple of minutes, then you're too fast.
I'd agree that I-80 through Wyoming isn't nearly as bad as I-70, and that's also true of I-40 through Albuquerque.