The slope of the line determines the date, and the closeness of fit is a measure of the statistical reliability of the resulting date.
Technical details on how these dates are calculated are given in Radiometric dating. As with any experimental procedure in any field of science, these measurements are subject to certain "glitches" and "anomalies," as noted in the literature.
C14 is continually being created and decaying, leading to an equilibrium state in the atmosphere.
Uranium 235 decay to lead has a half-life of 713 million years, so it is well suited to dating the universe.
Archaeologists deal in millions, thousands or, with luck, a few hundred.
Carbon dating has been the preferred technique since about 1950.
Radioactive carbon (Carbon 14) is formed in the upper atmosphere as a byproduct of cosmic radiation.
Cosmic rays are positively charged atoms moving at enormous speeds.