These types of questions should be solved directly through Algebrator. Links to the trial version will be included in this reply, please use the free trial version if you do not own a copy of Algebrator. Press the "Wizard" button, expand the "Line" category and choose the appropriate wizard.

Lines are parallel if their slopes are equal; lines are perpendicular if their slopes are inverse and opposite of each other. Graphing each pair of equations will therefore provide enough information to answer the problems since the standard graphical form of a linear equation is "y=mx+b", from which 'm' may easily be determined by inspection. The lines "y=2x+b" and 'y=-x/2 +b' are perpendicular lines because their slopes are '2' and '-1/2'.

Windows: https://www.softmath.com/tr/alg51win-tr-en.exe

Mac: https://www.softmath.com/tr/alg51mac-tr-en.dmg