In a physics laboratory experiment to verify the conservation of linear momentum, a cart of mass \(m_1\) travels along a horizontal, low-friction track with a constant initial speed \(v_0\). The cart collides with and latches onto a stationary target cart of mass \(m_2\), after which both carts move together with final speed \(v_f\). The experiment is repeated for several trials using different values of \(m_2\), while \(m_1\) and \(v_0\) remain unchanged across all trials. Which of the following pairs of quantities, when plotted on the vertical and horizontal axes, will yield a linear graph that confirms linear momentum is conserved, and what is the theoretical slope of the best-fit line?