The relationship between a freely falling object's gravitational potential energy (GPE) and its height from the ground is linear. GPE can be calculated using the formula:
\[ \text{GPE} = mgh \]
where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , m/s^2 \) on Earth's surface),
- \( h \) is the height of the object above the ground.
As the height \( h \) increases, the gravitational potential energy also increases proportionally, assuming mass and gravitational acceleration remain constant.
Therefore, the correct graph would show a straight line with a positive slope, starting from the origin (0,0) and rising as height increases. If you have a specific set of graphs, the one that accurately represents this linear relationship would be the correct choice.