Final answer:
Option A is the correct answer, illustrating direct variation where the circumference of a circle varies directly with the radius and the constant of variation is 2π.
Step-by-step explanation:
The scenario that illustrates direct variation is: A) The circumference of a circle varies directly with the radius (Constant = 2π). A direct variation exists when two quantities have a proportional relationship, such that when one quantity changes, the other changes by a constant factor. The constant of variation, in this case, is 2π, which represents the constant ratio between the circumference (C) and radius (r) of a circle, described by the formula C = 2πr. This indicates that for every unit increase in the radius, the circumference increases by 2π units.
In contrast, B) is incorrect because while an average varies directly with the sum of two numbers, it does not vary directly with either number alone. C) is incorrect because the slope of a line is a constant for a given line and does not vary with the y-intercept. And D) suggests a direct variation, but asking for the distance from zero, it implies absolute value, which is a different type of relationship than direct variation.