In a recent work, a new linear adaptive controller based on certainty-equivalence and backstepping design, which promises a level of transient and asymptotic performance comparable to that of the tuning functions adaptive backstepping controller without using high order nonlinearities, was proposed for linear time invariant systems. The proposal was supplemented with robustness and performance analysis in the presence of modeling uncertainties. In this note, the same idea is used to develop a new linear adaptive controller for slowly time varying systems with modeling uncertainties. The new adaptive control scheme guarantees robustness with respect to modeling errors via normalizing damping, parameter projection, and static normalization. Use of normalizing damping is essential in protecting the "linearity" of the system, which plays a key role in reaching the stability and robustness results.