In an experiment to determine the spring constant \(k\) of an ideal vertical spring, a student places various known masses \(m\) onto a tray of unknown mass \(m_0\) attached to the bottom of the spring. The period \(T\) of small vertical oscillations is measured for each mass \(m\). To obtain a linear relationship that accounts for the unknown mass \(m_0\), which quantities should be plotted on the vertical and horizontal axes, and how is \(k\) determined from the slope \(S\) of the line of best fit?