Perpendicular lines have negative reciprocals. This means that if you multiply the slopes of both lines, the product will be a -1.
In your given point-slope equation, the slope is 1/3. Therefore, the negative reciprocal of 1/3 must be -3.
Out of the given options:
y + 2 = -3(x — 4)
y = -3x - 5
are the linear equations that are perpendicular to y — 1 = 1/3(x + 2).
Therefore, the correct answers are Options 1 and 3.
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