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.
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).
Its composition would be represented as a single point on the isochron plot: Note that the above is somewhat simplified.
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.
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.