The formula for E that I'm using doesn't make sense to me but appears right in my notes and text book: E = lambda (charge per unit length)/2*pi*r*epsilon(permittivity of free space)

I wouldn't think E relies on r (for a straight line of charge). Aren't field lines parallel for a line of charge? Meaning E is constant at any point in the field?

I'm not given the r value for the final state of the particle, so I can't work out either E or the unknown y on the right hand side of that formula.

The "Electric Field Lines" are spread out more (1-dim), farther from the wire.
That means the E-field strength decreases as 1/r .
You need substripts to distinguish "E_final" from "E_initial" ... not equal!

You want to integrate E(r) from y_initial to y_final ...
or if this isn't for calc-based physics, use Potential.

No, still confused out of my brain. Was doing it on Mastering Physics.com, but exceeded attempts and failed the question. I tried a billion random different formulas. Worst thing is having no idea if they were even valid to use in an equation

The answer was apparently 0.134 m, but I still can't see how. I'll probably have to see tutorial teacher or something