Linear prediction has long played an important role in speech processing, especially in the development during the late 1960s of the first low bit rate speech compression/coding systems. The approach, which eventually became known as linear predictive coding (LPC), coincidentally came to fruition at the right time to be adopted as the speech compression technique in the first successful realtime packet speech communication through the nascent ARPAnet in December 1974 - the ancestor of voice over the Internet Protocol (IP) and, more generally, of realtime signal processing through the Internet. This first part of a two part monograph on LPC and the IP provides a tutorial overview of linear prediction and its application to speech coding. A variety of viewpoints provides background and context for the second part, which comprises a technical and personal history of LPC, its use in the first packet speech demonstrations, and many related stories of the early applications of LPC and the prehistory of the Internet.