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.
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Isochron dating requires a fourth measurement to be taken, which is the amount of a different isotope of the same element as the daughter product of radioactive decay.
Geology is the study of the composition and physical properties of rocks, minerals, gems and other related earth materials, including diamonds and crystals.
Scientists gain an understanding of the Earth's history by studying its composition.
However, the methods must be used with care -- and one should be cautious about investing much confidence in the resulting age...
especially in absence of cross-checks by different methods, or if presented without sufficient information to judge the context in which it was obtained.