two parallel lines have the same slope, the slop is the number accompains the x, so is -1/4
the general form of the line is
[tex]y=mx+b[/tex]I can replace the slope and the point (-4,-2) to find b
[tex]\begin{gathered} (-2)=(-\frac{1}{4})(-4)+b \\ -2=1+b \\ b=-2-1 \\ b=-3 \end{gathered}[/tex]so, the new parallel line is
[tex]y=-\frac{1}{4}x-3[/tex]