Parallel Lines

Parallel Lines

Parallel lines

What are parallel lines?

• Parallel lines are straight lines with the same gradient

  • Two parallel lines will never meet

    • They just stay side-by-side forever

• The equation of the line parallel to y  = mx  + c  is y  = mx  + d

  • $y=2x+1$ and $y=2x+5$ are parallel

  • $y=2x+1$ and $y=3x+1$ are not parallel

How do I find the equation of a parallel line?

• For example, to find the equation of the line parallel to y  = 2x  + 1 which passes through the point (3, 14)

  • write the parallel line as y  = 2x  + d

    • using the same gradient of 2

  • substitute x  = 3 and y  = 14 into this equation

    • 14 = 2 × 3 + d

    • 14 = 6 + d

  • solve to find d

    • d  = 8

  • The equation is y  = 2x  + 8