Parallel-Lines Aqa Foundation

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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
- $y equals 2 x plus 1$ and $y equals 2 x plus 5$ are parallel
- $y equals 2 x plus 1$ and $y equals 3 x plus 1$ 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

Worked Example

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

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

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Maths Gcse Aqa Foundation

Parallel-Lines Aqa Foundation

Parallel lines

What are parallel lines?

How do I find the equation of a parallel line?

Worked Example

Responses