Two lines that are parallel have the same slope. In its slope-intersect form, we can write the equation of a line with slope m and y-intercept b as:
[tex]y=mx+b[/tex]Step 1
Write the given equation in slope-intercept form and identify its slope m.
[tex]\begin{gathered} 2x+y=-8 \\ \\ 2x+y-2x=-2x-8 \\ \\ y=-2x-8 \end{gathered}[/tex]Thus:
[tex]m=-2[/tex]Step 2
Find the equation with the same slope m = -2. We need to identify which of them has -2 multiplying the variable x.
Answer
From the given options, the only one with the same slope m = -2, therefore parallel to the given line, is:
[tex]y=-2x+5\text{ (option B)}[/tex]