Question

which equation represents a line that is perpendicular to the line represented by the equation y=3/4x-1/2
a) y=2x-3/4
b) y=3/4x+1/2…

Answer 1

A line perpendicular to y=3/4x-1/2 will be of the form ...

y = -4/3x +c

Answer 2

Any line perpendicular to this line which has slope 3/4 must have
slope -4/3

Now y = 2x - 3/4 has slope 2 and so is not perpendicular to the
given line.

y=3/4x+1/2 has the same slope 3/4 as the given line and is therefore parallel to the given line.

So neither a) nor b) is perpendicular to the given line.