Given that the equation of line a is given by y = -2x + 3.
For parallel lines, the slopes are equal, thus the equation of a line parallel to line a will be given by y = -2x + c where c is an arbitrary constant.
For perpendicular lines, the slope of the second line is given by
, thus the slope of the line perpendicular to line a is
and the equation of the line is given by
, where c is an arbitrary constant.
Therefore, for the given equations:
y = 2x - 1 is neither parallel nor perpendicular to line a.
y = -2x + 5 is parallel to line a
is perpendicular to line a.