From:
[tex]\begin{gathered} y=2x+2 \\ m1=2 \end{gathered}[/tex]Since they are parallel, then:
[tex]\begin{gathered} m1=m2 \\ m2=2 \end{gathered}[/tex]Let:
[tex](x1,y1)=(-1,3)[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m2(x-x1) \\ y-3=2(x-(-1)) \\ y-3=2(x+2) \\ y-3=2x+2 \\ y=2x+5 \end{gathered}[/tex]