Order the steps for using Gauss’s law to find the field of an infinite charged line.

Use symmetry: the field must point radially outward, same at equal radii
Choose a coaxial cylinder as the Gaussian surface
Set the flux equal to $\lambda L/\varepsilon_0$ and solve for $E$
Write the side-wall flux as $E \cdot 2\pi r L$
Argue the flat end-caps contribute zero flux

Hints

Gauss’s law is only useful once symmetry has already told you the field’s direction and where its magnitude is constant.
The surface is chosen to match the symmetry, caps perpendicular to the field give zero flux, walls parallel give $EA$ .

Show the answer

Use symmetry: the field must point radially outward, same at equal radii
Choose a coaxial cylinder as the Gaussian surface
Argue the flat end-caps contribute zero flux
Write the side-wall flux as $E \cdot 2\pi r L$
Set the flux equal to $\lambda L/\varepsilon_0$ and solve for $E$

Why

Symmetry first, surface second, algebra last. The result, $E = \lambda/2\pi\varepsilon_0 r$ , falls off as $1/r$ , slower than a point charge’s $1/r^{2}$ , because fresh charge keeps "coming into view" as you back away from an infinite line.

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Order the steps for using Gauss’s law to find the field of an infinite charged line.

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