Students conduct an experiment to determine the electric permittivity of free space \(\varepsilon_0\) using an air-filled parallel-plate capacitor with fixed plate area \(A\). The students vary the plate separation distance \(d\) and measure the resulting capacitance \(C\) for each trial. Which of the following identifies the quantities that should be plotted on the vertical and horizontal axes to produce a linear graph, and gives the correct expression for \(\varepsilon_0\) in terms of the best-fit line's slope \(m\) and the plate area \(A\)?