Every drawing linear graphs question from 4 Cambridge IGCSE Mathematics (0580) past papers (May/June 2025 to May/June 2026), syllabus section 3.2. 4 questions covering Core and Extended tiers, ordered from Core to Extended. Each question is labelled with its question paper code (for example 0580/23/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 Drawing Linear Graphs past paper questions: Core (Papers 1 and 3)
May/June 2026 · Paper 3 · 0580/33/M/J/26 · Q21(a)
On the axes, sketch the graph of y = 3x − 2.
Show solution
- Compare y = 3x − 2 with y = mx + c: the gradient m = 3 and the y-intercept c = −2.
- A positive gradient means the line slopes upwards from left to right.
- Sketch a straight line sloping upwards that crosses the y-axis below the origin, at −2
Feb/Mar 2026 · Paper 3 · 0580/32/F/M/26 · Q18
(a) On the grid, draw the graph of y = 0.5x + 3 for −4 ≤ x ≤ 4.
(b) Write down the equation of the line that passes through the point (0, 7) and has gradient 0.
Show solution
- Make a table of values for y = 0.5x + 3.
- x = −4: y = −2 + 3 = 1. x = 0: y = 3. x = 4: y = 2 + 3 = 5.
- Plot (−4, 1), (0, 3) and (4, 5) and join them with a ruler.
- A gradient of 0 means the line is flat (horizontal), so every point has the same y-value.
- It passes through (0, 7), so the equation is y = 7
0580 Drawing Linear Graphs past paper questions: Extended (Papers 2 and 4)
May/June 2026 · Paper 2 · 0580/23/M/J/26 · Q8
The line L is shown on the grid.
(a) Find the gradient of line L. (b) On the grid, draw the line y − 2x + 3 = 0.
Show solution
- Pick two points where line L crosses the grid exactly. Between them, the line goes down 2 squares for every 3 squares across.
- Gradient = change in y⁄change in x = −2⁄3
- Gradient = −2⁄3
- Rearrange the equation into y = mx + c: y − 2x + 3 = 0 becomes y = 2x − 3.
- It crosses the y-axis at −3, and goes up 2 for every 1 across.
- Plot the points and join them with a ruler: (0, −3), (1, −1), (2, 1) and (3, 3)
May/June 2025 · Paper 2 · 0580/21/M/J/25 · Q6
The line x + y = 7 is drawn on the grid.
(a) On the grid, draw the line y = 2x + 1.
(b) Use your graph to solve these simultaneous equations. x + y = 7 and y = 2x + 1
Show solution
- Make a table of values for y = 2x + 1: x = 0 gives y = 1, x = 1 gives 3, x = 2 gives 5, x = 3 gives 7.
- Plot the points and join them with a ruler.
- A ruled straight line through (0, 1) and (3, 7).
- The solution of the simultaneous equations is the point where the two lines cross.
- Read the coordinates of the crossing point: x = 2, y = 5
- Check: 2 + 5 = 7 ✓ and 2 × 2 + 1 = 5 ✓
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