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If the slopes of two lines are unequal, they will cross somewhere, so the distance between them depends on x, and isn't really defined.If the slopes are equal, they are parallel, so they don't cross. So two lines are far apart if they have the same slope and a large difference in their x or y intercepts.
Relief
lines that are beside each other and never meet
Perpendicular and parallel lines are two examples.
That's the only kind of parallel lines there are, non-intersecting!