IGCSE Maths 0580 Parallel Lines Past Paper Questions and Worked Solutions

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IGCSE Maths (0580) · Coordinate Geometry · 3.6

Every parallel lines question from 3 Cambridge IGCSE Mathematics (0580) past papers (May/June 2025 to May/June 2026), syllabus section 3.6. 3 Core-tier questions. Each question is labelled with its question paper code (for example 0580/31/M/J/26) and every final answer matches the official Cambridge mark scheme. Try each question first, then click “Show solution” to check your working. This page is part of our IGCSE Maths 0580 Coordinate Geometry past paper questions.

0580 Parallel Lines past paper questions: Core (Papers 1 and 3)

12 marksCore

May/June 2026 · Paper 3 · 0580/31/M/J/26 · Q27

Find the equation of the line parallel to y = 4x + 3 that passes through (2, 9).

Show solution
  1. Parallel lines have the same gradient. The gradient of y = 4x + 3 is 4, so the new line is y = 4x + c.
  2. It passes through (2, 9): 9 = 4 × 2 + c, so 9 = 8 + c and c = 1.
  3. y = 4x + 1
Answer y = 4x + 1
25 marksCore

Oct/Nov 2025 · Paper 3 · 0580/32/O/N/25 · Q25

(a) Line L crosses the y-axis at 2 and rises 1 for every 4 across. Find the equation of line L in the form y = mx + c.

0580/32 October/November 2025 Q25(a) – line L on a grid from 0 to 10xy1234567891012345L

(b) Another line, R, has equation y = −3x + 5. Find the equation of the line which is parallel to R and goes through the point (1, 5). Give your answer in the form y = mx + c.

Show solution
Part (a)
  1. Gradient = rise ÷ run = 1 ÷ 4 = 1⁄4.
  2. The line crosses the y-axis at 2, so c = 2.
  3. y = 1⁄4x + 2
Answer y = 1⁄4x + 2
Part (b)
  1. Parallel lines have the same gradient. R has gradient −3, so the new line is y = −3x + c.
  2. Substitute (1, 5): 5 = −3 × 1 + c, so 5 = −3 + c and c = 8.
  3. y = −3x + 8
Answer y = −3x + 8
33 marksCore

May/June 2025 · Paper 1 · 0580/13/M/J/25 · Q10

(a) Line A has equation y = 3x + 1. Line B has equation y = 3x − 1. Draw a ring around the description that is correct: Line A intersects line B / Line A has a steeper gradient than line B / Line A is perpendicular to line B / Line A is parallel to line B / Line A and line B intersect the y-axis at the same point.

(b) On the grid, draw the graph of y = 2x − 1.

0580/13 May/June 2025 Q10 – coordinate grid from −5 to 5 for y = 2x − 1xy-5-4-3-2-112345-5-4-3-2-1123450
Show solution
Part (a)
  1. In y = mx + c, m is the gradient and c is where the line crosses the y-axis.
  2. Line A: gradient 3, crosses at 1. Line B: gradient 3, crosses at −1.
  3. Same gradient and different crossing points means the lines never meet: Line A is parallel to line B
Answer Line A is parallel to line B
Part (b)
  1. Make a table of values for y = 2x − 1.
  2. x = 0: y = −1. x = 1: y = 1. x = 2: y = 3.
  3. Plot the points and join them with a ruler across the grid.
  4. A ruled straight line through (0, −1), (1, 1) and (2, 3).
0580/13 May/June 2025 Q10 solution – straight line y = 2x − 1xy-5-4-3-2-112345-5-4-3-2-1123450y = 2x − 1
Answer A ruled straight line through (0, −1), (1, 1) and (2, 3).

Question papers used on this page

All parallel lines questions above, listed by 0580 question paper code.

QP codeFile namePaperQuestions
0580/31/M/J/260580_s26_qp_31May/June 2026 · Paper 3 (Core)Q27
0580/32/O/N/250580_w25_qp_32Oct/Nov 2025 · Paper 3 (Core)Q25
0580/13/M/J/250580_s25_qp_13May/June 2025 · Paper 1 (Core)Q10

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