COO011 · Coordinate geometry · Classes 9–11
Parallel lines
Parallel lines have equal slopes and never meet. The distance between y = mx + c₁ and y = mx + c₂ is |c₁ − c₂| / √(1 + m²).
∥Parallel lines
📐 Formula
m₁ = m₂; d = |c₁ − c₂| / √(1 + m²)
✏️ Worked example
y = 2x + 3 and y = 2x − 2: gap = 5/√5 ≈ 2.24.
🌍 Where it is used
Railway tracks, lanes, ruled paper.
❓ Quick check
Which is parallel to y = 3x + 1?
🏋️ Practice
EasySlope of a line parallel to 2y = 4x + 1?
Answer: 2
MediumLine through (0, 4) parallel to y = −x?
Answer: y = −x + 4
ChallengeDistance between y = 1 and y = 6?
Answer: 5