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Answer:
[tex]\boxed {\boxed {\sf B. \ y= - \frac{1}{2} x-4}}[/tex]
Step-by-step explanation:
We are given the line y=2x+8. It is in slope-intercept form or y= mx+b, where m is the slope and b is the y-intercept.
The slope of the line is 2.
We want to find the equation that is perpendicular. Perpendicular lines have negative reciprocal slopes.
1. Negate
2. Reciprocal
The perpendicular slope is -1/2, so the correct equation must be B.