According to Gauss's Law, for an infinitely long cylindrical charge distribution (or a line charge) with linear charge density $\lambda$ (given here as charge $q$ per unit length), the electric field $E$ at a distance $r$ from the axis (where $r > R$) is determined by considering a coaxial cylindrical Gaussian surface of radius $r$ and length $l$.

The electric flux is $\Phi_E = E \cdot (2\pi r l)$. The enclosed charge is $q_{enc} = q \cdot l$ (since $q$ is charge per unit length). Applying Gauss's Law: $E (2\pi r l) = \frac{q l}{\epsilon_0}$. Solving for $E$, we get $E = \frac{q}{2\pi\epsilon_0 r}$. Thus, the electric intensity is inversely proportional to the distance $r$ ($E \propto \frac{1}{r}$).