Final answer:
A justice who agrees with the majority decision of the Supreme Court but for different reasons writes a concurring opinion, which provides alternative legal reasoning to the case.
Step-by-step explanation:
When a justice agrees with the majority decision of the Supreme Court but has different reasons for their agreement, they may choose to write a concurring opinion. This concurring opinion highlights the separate legal reasoning or different principles the justice feels are important to the case at hand. While the majority opinion sets forth the official reasoning of the court's decision, the concurring opinion serves to provide an alternative perspective or supplement the majority's rationale.
Justices in the minority, who disagree with the majority decision, may write dissenting opinions. These opinions can potentially influence future cases, as they provide a record of alternative legal philosophies and might be used as a basis for overturning precedent in later decisions.