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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Various radioactive elements are involved, including Carbon-14, Uranium-238, Thorium-232, and Potassium-40.
In a related article on geologic ages (Ages), we presented a chart with the various geologic eras and their ages.
In a separate article (Radiometric dating), we sketched in some technical detail how these dates are calculated using radiometric dating techniques.
By looking at other outcrops in the area, our geologist is able to draw a geological map which records how the rocks are related to each other in the field.
From the mapped field relationships, it is a simple matter to work out a geological cross-section and the relative timing of the geologic events.