When their slopes are of the same value and their y intercepts are different
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No, only lines that have the same slope can be parallel.
The slopes of two parallel lines will be the same.
Two lines are parallel if and only if they have the same slope. Two lines are perpendicular if the product of their slopes is -1. If neither of these conditions are met, the lines are nether parallel, or perpendicular.
The same slope
If two lines are parallel, they have the same slope.(And if they are perpendicular, the product of their slopes is minus one - unless one line is horizontal and the other vertical.)