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Rule

# Parallel Lines

Lines in the same plane that never intersect are called parallel lines. Lines are parallel if and only if they have the same slope. It follows, then, that all horizontal lines are parallel to one another, as are all vertical lines. Two lines written in slope-intercept form, $y=mx+b,$ are parallel if their slopes, $m,$ are equal and they have different $y$-intercepts, $b.$

$m_1 = m_2 \quad \text{and}\quad b_1 \neq b_2$

In the diagram, it can be seen that two lines with the same slope never intersect.
Parallel lines must have different $y$-intercepts. Otherwise they would be identical and have an infinite number of intersecting points.