Question

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Answer 1

two lines are parallel only if they have the same slope
the slope of
\[y=\frac{1}{x}x+1\] is \(\frac{1}{3}\) and the slope of
\[y=-3x+4\] is \(-3\) so the student is an idiot who does not realize that
\[\frac{1}{3}\neq -3\]

Answer 2

on the other hand, \(-3\) is the "negative reciprocal" of \(\frac{1}{3}\) so in fact the lines are "perpendicular"