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Parallel Lines

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,y=mx+b, are parallel if their slopes, m,m, are equal and they have different yy-intercepts, b.b.

m1=m2andb1b2 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 yy-intercepts. Otherwise they would be identical and have an infinite number of intersecting points.
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