Yes
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Take any two lines and look at their slopes. -- If the slopes are equal, then the lines are parallel. -- If the product of the slopes is -1, then the lines are perpendicular.
equal
Lines with equal slopes are parallel, because they are going the same direction. If the slope and the intercept are the same, the lines are coinciding, because they are on top of each other.
They're parallel if their slopes are equal.
same slopes = parallel lines