Robinson Tuition
Grade 6 · Higher · free GCSE maths worksheet

Parallel lines equations

Lines with equal gradients.

12 original questions, 34 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Here are the equations of four straight lines.

A: y = 2x - 5

B: y = x + 1

C: y = 3 - 2x

D: 2y = x + 4

Write down the letter of the line that is parallel to y = 2x + 1

1 mark
Show answer
A
2

Show that the straight lines with equations y = 3x + 2 and 6x - 2y = 5 are parallel.

2 marks
Show answer
Rearranging 6x - 2y = 5 gives y = 3x - 52; both gradients are 3, so the lines are parallel
3

Sam says that the straight lines with equations y = 5x - 1 and 5y = x + 10 are parallel.

Is Sam correct? You must explain your answer.

2 marks
Show answer
No: 5y = x + 10 rearranges to y = x5 + 2, so the gradients are 5 and 15, which are not equal
4

The straight line L has equation y = 4x + 1

Find the equation of the straight line that is parallel to L and passes through the point (2, 3).

2 marks
Show answer
y = 4x - 5
5

A straight line has equation y = -2x + 5

Find the equation of the straight line that is parallel to this line and passes through the point (3, -2).

3 marks
Show answer
y = -2x + 4
6

The line with equation y = 3x + 5 is parallel to the line with equation y = (2k - 1)x + 2

Work out the value of k.

2 marks
Show answer
k = 2
7

The straight line L has equation y = 5x - 3

  1. Write down the gradient of L.
  2. Find the equation of the straight line that is parallel to L and passes through the point (2, 11).
4 marks
Show answer
a) 5 b) y = 5x + 1
8

The straight line L has equation 3x + 4y = 8

Find the equation of the straight line that is parallel to L and passes through the point (8, 1).

4 marks
Show answer
y = -3x4 + 7
9

The line with equation 4x + 2y = 7 is parallel to the line with equation y = kx - 1

Work out the value of k.

3 marks
Show answer
k = -2
10

A straight line has equation 6x - 3y = 5

Find the equation of the straight line that is parallel to this line and passes through the point (1, 4).

3 marks
Show answer
y = 2x + 2
11

Line A passes through the points (0, 5) and (4, 13).

Line B is parallel to line A and passes through the point (3, -1).

  1. Find the equation of line B.
  2. Show that the point (5, 3) lies on line B.
4 marks
Show answer
a) y = 2x - 7 b) When x = 5, y = 2 × 5 - 7 = 3, so (5, 3) lies on line B
12

A is the point (1, 2), B is (5, 4), C is (6, 7) and D is (2, 5).

Show that ABCD has two pairs of parallel sides.

4 marks
Show answer
AB and DC both have gradient 1/2; AD and BC both have gradient 3

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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