Answer:
(d) y' = 3/2x
Explanation:
The transformation for rotating a figure 180° about the origin is ...
(x, y) ⇒ (-x, -y)
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Given the line ...
y = 3/2x
The translation of it is ...
-y' = 3/2(-x)
Simplifying gives ...
y' = 3/2x
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Additional comment
Rotation 180° about the origin is equivalent to reflection across the origin. For a line that passes through the origin, that reflection is simply the original line, as we can see in the equations above.