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Parallel Lines

Two lines are parallel if they have the same gradient and neither share common points. This means that they never intersect each other. For lines in the slope-intercept form y=mx+cy=mx+c, this means that their slopes m1m_1 and m2m_2 are the same.

m1=m2 m_1 = m_2

Parallel lines in a coordinate system do not have the same y-intercept because then they would be identical and have an infinite number of intersecting points.