Final answer:
The equation that represents the amount of juice that remains after x students are served is y = 32 - x.
Step-by-step explanation:
The equation that represents the amount of juice that remains after x students are served is y = 32 - x. The teacher starts with a 2-gallon (32-cup) container of juice. Each student is served 1 cup of juice, which means the amount of juice that remains decreases by 1 cup for each student served. The equation y = 32 - x represents this relationship, where y represents the remaining amount of juice and x represents the number of students served.