In an experiment to determine the local acceleration due to gravity \(g\), students set up an Atwood machine consisting of two blocks of masses \(m_1\) and \(m_2\) connected by a light string over a pulley with negligible rotational inertia. A constant bearing friction force \(f\) opposes the motion of the string. The total mass of the system, \(M = m_1 + m_2\), is kept constant while mass is transferred between the blocks to vary the mass difference \(\Delta m = m_1 - m_2\), and the resulting acceleration \(a\) is measured for each trial where the system accelerates. To determine \(g\) directly from the slope of a best-fit line, which quantities should be plotted on the vertical and horizontal axes, and what is the physical meaning of the horizontal intercept of this line?