The acceleration due to gravity ($g$) varies with the distance ($r$) from the centre of the Earth as follows:

1. Inside the Earth ($r < R$): Assuming the Earth to be a sphere of uniform density, $g$ is directly proportional to the distance from the centre. The formula is $g = \frac{GM}{R^3}r$, which implies $g \propto r$. This relationship is represented by a straight line passing through the origin and increasing up to the surface.
2. At the Surface ($r = R$): The value of $g$ is maximum, $g = \frac{GM}{R^2}$.
3. Outside the Earth ($r > R$): The value of $g$ decreases as the distance increases, following the inverse square law. The formula is $g = \frac{GM}{r^2}$, which implies $g \propto \frac{1}{r^2}$. This is represented by a curve (hyperbola) decreasing asymptotically towards zero.

Therefore, the correct graph shows a linear increase for $r < R$ and a curvilinear decrease for $r > R$.