The relationship between acceleration due to gravity (g) and mass (m) for objects near the surface of the Earth is independent. This means that the acceleration due to gravity is the same for all objects, regardless of their mass.

Here's why:

* Newton's Law of Universal Gravitation: The force of gravity between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.

* Near Earth's surface: The distance between the object and the Earth's center is essentially constant.

* Acceleration due to gravity: This is the acceleration experienced by an object due to the Earth's gravitational pull. It is determined by the Earth's mass and radius, not the object's mass.

Therefore, the graph representing the relationship between acceleration due to gravity and mass would be a horizontal line. This indicates that the value of acceleration due to gravity remains constant (approximately 9.8 m/s²) regardless of the mass of the object.