Saving is the excess of deferred over anticipated consumption, and its dependence on income is much as described by Keynes (see The General Theory), but in classical theory definitely an increasing function of "r". (The dependence of "s" on income "y" was not relevant to classical concerns prior to the development of theories of unemployment.) The rate of interest is given by the intersection of the solid red saving curve with the blue investment schedule. But so long as the investment schedule is almost vertical, a change in income (leading in extreme cases to the broken red saving curve) will make little difference to the interest rate.