What practical examples are there of uses of the real number line in everyday life?
Mechanical devices for measuring.
Most mechanical devices for measuring contain part of the real number line.
The most obvious one we use daily is a thermometer - the temperature can increase from freezing point, but it is possible to have negative temperatures as well.
You can read your altitude on the screen of a GPS unit - it will tell you how high or even how far below sea level you are.