Parallel Lines (Edexcel IGCSE Maths)

Spec point — 4.1B

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 = 2*x * + 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

Worked Example Find the equation of the line that passes through the point (2, 1), which is parallel to the straight line $y=3x+7$.

Answer:

Parallel means the gradient will be the same Use y = mx + d where m = 3

$y=3x+d$

Substitute in x = 2 and y = 1

$1=3\times2+d$

Simplify the equation

$1=6+d$

Solve the equation to find d (by subtracting 6 from both sides)

$-5=d$

*Write out the final answer in the form y = mx + d *

$y=3x-5$