The relationship between an object's gravitational potential energy (GPE) and its height above the ground can be represented by a linear graph. The gravitational potential energy (GPE) of an object at height \( h \) is given by the formula:
\[ \text{GPE} = mgh \]
where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \) near the Earth's surface),
- \( h \) is the height above the ground.
From this equation, we can see that GPE is directly proportional to height \( h \). Therefore, if you plot gravitational potential energy on the y-axis and height on the x-axis, the graph will be a straight line that starts from the origin (0, 0) and increases linearly with height.
If you are looking at multiple graphs, the correct one will be the one that depicts a straight line with a positive slope, indicating that as height increases, gravitational potential energy also increases.