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Consider some molten rock in which isotopes and elements are distributed in a reasonably homogeneous manner.
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.
(For brevity's sake, hereafter I will refer to the parent isotope as ).
In addition, it requires that these measurements be taken from several different objects which all formed at the same time from a common pool of materials.
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.
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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.