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Parallel Lines in the Coordinate Plane

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About This Diagram

This diagram shows three parallel lines in the coordinate plane, demonstrating that parallel lines have equal slopes but different y-intercepts. Hover over any line to highlight it.

Lines Shown

Line Equation Slope (m) Y-intercept (b)
1 y = 2x + 4 2 4
2 y = 2x 2 0
3 y = 2x - 3 2 -3

Key Observations

  • All three lines have the same slope (m = 2)
  • They have different y-intercepts (b = 4, 0, -3)
  • The lines never intersect
  • They remain the same distance apart throughout

Parallel Lines Theorem

Two non-vertical lines are parallel if and only if they have equal slopes: m₁ = m₂

Learning Objectives

  • Understand that parallel lines have equal slopes
  • Apply the parallel lines theorem to identify parallel lines

Bloom's Taxonomy Level

Understanding and Applying - Slope comparison and identification.

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