(Rocks which include several different minerals are excellent for this.) Each group of measurements is plotted as a data point on a graph.
The X-axis of the graph is the ratio of in a closed system over time.
Consider some molten rock in which isotopes and elements are distributed in a reasonably homogeneous manner.
Its composition would be represented as a single point on the isochron plot: Note that the above is somewhat simplified.
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.
A routine statistical operation on the set of data yields both a slope of the best-fit line (an age) and a variance in the slope (an uncertainty in the age).
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.There are minor differences between isotopes of the same element, and in relatively rare circumstances it is possible to obtain some amount of differentiation between them. The effect is almost always a very small departure from homogeneous distribution of the isotopes -- perhaps enough to introduce an error of 0.002 half-lives in a non-isochron age. but it is rare and the effect is not large enough to account for extremely old ages on supposedly young formations.) as minerals form.This results in a range of X-values for the data points representing individual minerals.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.
The simplest form of isotopic age computation involves substituting three measurements into an equation of four variables, and solving for the fourth.