Whether there's a data point on the Y-axis or not, the Y-intercept of the line doesn't change as the slope of the isochron line does (as shown in Figure 5).
Therefore, the Y-intercept of the isochron line gives the initial global ratio of could be subtracted out of each sample, and it would then be possible to derive a simple age (by the equation introduced in the first section of this document) for each sample.
An additional nice feature of isochron ages is that an "uncertainty" in the age is automatically computed from the fit of the data to a line.
Use of half life in carbon dating
Note that the mere existence of these assumptions do not render the simpler dating methods entirely useless.
In many cases, there are independent cues (such as geologic setting or the chemistry of the specimen) which can suggest that such assumptions are entirely reasonable.
Unfortunately, one must wade through some hefty math in order to understand the procedures used to fit isochron lines to data.
General comments on "dating assumptions" All radiometric dating methods require, in order to produce accurate ages, certain initial conditions and lack of contamination over time.
Isochron methods avoid the problems which can potentially result from both of the above assumptions.