Final answer:
The equation of a tangent line is determined by the slope of the curve at the point of tangency, the point of tangency itself, and the equation of the curve.
Step-by-step explanation:
The equation of a tangent line to a curve at a given point is determined by several factors. First and foremost, the slope of the curve at the point of tangency is crucial, as the slope of the tangent line must be equal to the slope of the curve at that point. Additionally, you need to know the specific point of tangency because the tangent line must pass through this point. Lastly, the overall equation of the curve also plays a role in determining the equation of the tangent line since it provides the necessary information to compute the slope and confirm the point of tangency. The correct answer to the student's question, therefore, is d) All of the above.