How do I update the serial monitor without printing a new line each time?
The ultra-basic "serial monitor" in the Arduino IDE cannot do what you want.

Instead you need to either write a special client program, or use a more standard serial terminal program, such as Tera Term (Windows), Minicom (Linux), etc.

These standard serial terminal programs use a special sequence of characters called ANSI escape codes which manipulate the display, doing such things as setting colours, moving the cursor around, etc.

More information on ANSI escape codes can be found here: http://en.wikipedia.org/wiki/ANSI_escape_code