Parallel Lines

3.6 Parallel Lines – Cheat Sheet

1. Key Facts About Parallel Lines

• Parallel lines have the same gradient (m).
• If two lines are parallel: m₁ = m₂.
• Equation of a straight line in gradient–intercept form: y = mx + c.

2. Finding Equation of a Parallel Line

Steps:

1. Identify the gradient from the given line.
2. Use point–slope form: y − y₁ = m(x − x₁).
3. Substitute given point and gradient.
4. Rearrange to y = mx + c form.

3. Worked Example

Example: Find equation of the line parallel to y = 4x − 1 that passes through (1, −3)

• Gradient m = 4 (same as given line).
• Use y − y₁ = m(x − x₁):
  y − (−3) = 4(x − 1)
  y + 3 = 4x − 4
  y = 4x − 7

4. Quick Examples Table