Linear GBAS operates on the premise that there is a direct, proportional relationship between the dose of a chemical and the response it elicits. This is expressed through a linear equation, typically in the form of y = mx + c, where y represents the effect, x is the dose, m is the slope (signifying change in response per unit change in dose), and c is the intercept. This model helps in estimating the threshold limit and understanding how varying concentrations impact biological systems.