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 [tex]m_2=- \frac{1}{m_1} [/tex], thus the slope of the line perpendicular to line a is [tex]-\frac{1}{-2} = \frac{1}{2} [/tex] and the equation of the line is given by [tex]y= \frac{1}{2} x+c[/tex], 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
[tex]y= \frac{1}{2} x+7[/tex] is perpendicular to line a.
