Compare slopes of the lines
If the slopes are equal, the lines are parallel
For vertical lines, check whether both have undefined slope
Use corresponding angles with a transversal
If corresponding angles are equal, the lines are parallel
Use alternate interior angles with a transversal
If alternate interior angles are equal, the lines are parallel
Use same-side interior angles with a transversal
If same-side interior angles are supplementary, the lines are parallel
Check whether the lines have the same direction and never meet
Use coordinate geometry or graphing to verify equal slope and different intercepts