A group of students performs an experiment to determine the local acceleration due to gravity, \(g\). The students submerge a small pressure sensor to various depths \(d\) in an open container filled with a liquid of known uniform density \(\rho\). The absolute pressure measured by the sensor is modeled by the equation \(P = P_{\text{atm}} + \rho g d\), where \(P_{\text{atm}}\) is atmospheric pressure. If the students create a linear graph by plotting \(P\) on the vertical axis as a function of \(d\) on the horizontal axis, which of the following correctly relates the line of best fit to \(g\) and describes the physical meaning of the vertical intercept?