Isochron methods avoid the problems which can potentially result from both of the above assumptions.
The better the fit of the data to the line, the lower the uncertainty.
For further information on fitting of lines to data (also known as regression analysis), see: Note that the methods used by isotope geologists (as described by York) are much more complicated than those described by Gonick.
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.
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.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.Now that the mechanics of plotting an isochron have been described, we will discuss the potential problems of the "simple" dating method with respect to isochron methods.The amount of initial wouldn't change over time -- because it would have no parent atoms to produce daughter atoms.The wonderful property of isochron methods is: if one of these requirements is violated, it is nearly certain that the data will indicate the problem by failure to plot on a line.