\(x-2y=8\Leftrightarrow y=\dfrac{1}{2}x-4\)

Let the equation of the line through point P be \(y=\dfrac{1}{2}x+a\left(a\ne-4\right)\)

\(3=\dfrac{1}{2}.4+a\Leftrightarrow a=1\)

So, the answer is \(y=\dfrac{1}{2}x+1\)