This was, we can say, the whole huge first generation of BASIC, from 1964 to early 1990s. Very tipically, such BASICs shared the following characteristics:
GOTO 290
and from there execution followed sequentially until the end or another jump.Line numbers were inherited from the FORTRAN of the days when BASIC was created. They were usual in many other languages by then, and in fact the idea of a sequence of instructions and jumps comes very directly from machine code and Assembly.
Some newer BASICs kept support to numbered-line programming just for compatibility with older code, but did not really require line numbers to work anymore. These are not "line-numbered BASICs" in the context of this site.