Simple answer is yes. You must move over to the right hand lane since it is illegal to pass on the right of another vehicle. 346.08 When overtaking and passing on the right.
As a highway worker in Wisconsin that puts up the SLOWER TRAFFIC KEEP RIGHT sign, Wisconsin law 346.05(3) (3) Any vehicle proceeding upon a roadway at less than the normal speed of traffic at the time and place and under the conditions then existing shall be driven in the right-hand lane then available for traffic, or as close as practicable to the right-hand edge or curb of the roadway, except when overtaking and passing another vehicle proceeding in the same direction or when preparing for a left turn or U-turn at an intersection or a left turn into a private road or driveway, and except as provided in s. 346.072. In this section, "emergency or roadside service vehicle" (a) An authorized emergency vehicle giving visual signal.
(b) A tow truck flashing red lamps, as required by s. 347.26 (6) (b).
(c) Any road machinery or motor vehicle used in highway construction or maintenance displaying the lights specified in s. 347.23 (1) (a) or (b) or, with respect to a motor vehicle, displaying the lights specified in s. 347.26 (7).
In Texas New law requires "left lane for passing" signs
A law passed during the last legislative session requires that the Texas Department of Transportation put up signs that say "Left Lane for Passing Only" whenever the department needs to replace signs that say "Slower Traffic Keep Right."