Final answer:
The rule pertaining to the autonomous line is related to autonomous differential equations in mathematics, where the change of a variable is independent of the independent variable, such as time. An autonomous line represents the trajectory of a variable's change over time, depicted in a phase plane.
Step-by-step explanation:
The rule pertaining to the autonomous line likely refers to the concept of an autonomous differential equation in mathematics, particularly within the context of calculus or differential equations. An autonomous differential equation is a type of differential equation that does not explicitly depend on the independent variable, often time. In other words, the rate of change of a variable is a function of the variable itself but not of the independent variable.
For example, if we have a differential equation of the form dy/dx = f(y), then it is autonomous since the right-hand side of the equation is solely a function of y. A solution to this kind of equation, y(x), represents an autonomous line or a trajectory in the phase plane, which shows how the variable y evolves over time regardless of the actual value of the independent variable x.