Final answer:
The correct relationship between the number of batches of cookies (c) and the cups of sugar (s) is s = (2/3)c, which indicates that for every batch of cookies, 2/3 cups of sugar are required. However, none of the options provided exactly match this equation, and without the ability to adjust the options given, we cannot select a perfect match.
Step-by-step explanation:
The student's question asks for the relationship between the number of batches of cookies (c) and the cups of sugar (s) needed to make those batches.
This kind of problem requires setting up a proportional relationship, which is similar to constructing conversion factors in stoichiometric relationships, often encountered in science, particularly in cooking and chemistry. Given that Emily uses 4 cups of sugar to make 6 batches of cookies, we can write the proportion as 4 cups of sugar per 6 batches, which simplifies to 2/3 cups of sugar per batch.
Thus, the equation representing this relationship for Michael, who will make c batches of cookies using s cups of sugar, is s = (2/3)c. None of the provided options directly match this equation, but if we convert the fraction 2/3 to a decimal, it becomes approximately 0.666, which is not available in the options. If the objective is to present the findings in terms of the nearest given choice, without further context or adjustment of the options, we cannot confidently provide an exact match.