(For brevity's sake, hereafter I will refer to the parent isotope as ).
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.
This will be discussed in more detail in the section on Gill's paper below.
The "generic" method described by Gonick is easier to understand, but it does not handle such necessities as: (1) varying levels of uncertainty in the X- versus Y-measurements of the data; (2) computing an uncertainty in slope and Y-intercept from the data; and (3) testing whether the "fit" of the data to the line is good enough to imply that the isochron yields a valid age.
The simplest form of isotopic age computation involves substituting three measurements into an equation of four variables, and solving for the fourth.
The equation is the one which describes radioactive decay: If one of these assumptions has been violated, the simple computation above yields an incorrect age.