The \(K_m\) value is determined experimentally by measuring the reaction rate at different substrate concentrations. These data points are then plotted to form a Michaelis-Menten curve. The curve typically shows a hyperbolic shape where the initial reaction rate increases with substrate concentration but eventually plateaus. The \(K_m\) is derived from this curve by identifying the substrate concentration at which the reaction rate is half of the maximum velocity (Vmax).