We measure the real and imaginary conductivity σ(k=0,ω) of a high-mobility two-dimensional electron gas (2DEG) system at frequencies below and above the momentum scattering rate. The imaginary part of the 2DEG impedance is observed to be inductive, consistent with the Drude model. Using this kinetic inductance, we construct a transmission line by capacitively coupling the 2DEG to an Al Schottky barrier gate separated by 5000 Å from the 2DEG. The measured wave velocity and temperature-dependent damping of this transmission line are in good agreement with a simple Drude model. Exciting these modes is equivalent to exciting a 2D plasma mode strongly modified by the interaction between the 2DEG and the gate.