I am assuming that the two compounds are related in a stoichiometric way (either x moles of s2o3 is reacting with y moles of s2o8, or x moles of s2o3 is required to produce y moles of s2o8 in a reaction). For simplicity, I will explain it in terms of s2o3 producing s2o8, so it can be said that y moles of s2o8 are produced for every x moles of s2o3 spent. Because the number of moles of s2o8 produced can be expressed as some number times the number of moles of s2o3, we can treat it as a function y = kx where y is the moles of s2o8, k is the mole ratio and x is the moles of s2o3. In this case, the slope of the line defines the rate of change of x, so by differentiating the function you should get y' = k(slope of line) where y' is the rate of change in the number of moles of s2o8 and k is still the mole ratio.
Is this correct?