Why would car die on incline when low on gas?

Answer 1

When you drive on a slope the gas in your tank goes towards the back due to the slope and, well, gravity.

Due to the location of the fuel intake pipe in your gas tank, when there is a small amount of gas in the tank it will all be sitting in the back, and thus, unable to provide fuel for your engine, causing your car to stall and die.

To help further this point, an example may be necessary.

A man places a bottle of water on a incline. Where does the water go.

I'll leave you to think about what you've done.