Which of the following represents an explicit rule?

An explicit rule is a mathematical expression that defines a relationship between input and output variables directly, allowing one to compute the output for any given input. In this case, the expression "2x + 1 = y" serves as an explicit rule because it establishes a clear relationship between the variable x and the output y. By substituting any value of x into the equation, you can directly calculate the corresponding value of y, making it straightforward to identify how changes in x affect y.

This characterization distinguishes the expression from the other options. For instance, the first choice is merely an arithmetic operation that results in a single numerical value rather than establishing a variable relationship. The third choice, "y = 5 for all x," is a constant function that does not provide variability contingent upon x. Lastly, the fourth choice represents a quadratic equation rather than an explicit rule, as it focuses on the relationship between the variable and a specific set of solutions rather than defining y explicitly in terms of x. Thus, "2x + 1 = y" is the most fitting representation of an explicit rule among the given options.