Gradient from two points
Find the gradient of the line joining (−2, 7) and (3, 1).
- Change in y = 1 − 7 = −6
- Change in x = 3 − (−2) = 5
- Gradient = −6 ÷ 5
Answer: −6/5
Gradient & straight-line graphs
Gradient City
Mapped to the Cambridge IGCSE 0580 coordinate geometry section (C/E3.2–3.7) and GCSE A9–A10, with question types taken from recent papers: “find the equation of the line through two points”, “the gradient and y-intercept of 5x + 4y = 8”, “the perpendicular bisector of AB”.
What students practise
- Gradient from a grid (Core) and from two points (Extended)
- Tables of values and drawing y = mx + c and ax + by = c
- Where a line crosses the axes
- Gradient and y-intercept from y = mx + c and ax + by = c
- Equation of a line from a graph, two points, or a point and a gradient
- Parallel lines
- Perpendicular lines and the perpendicular bisector (Extended / Higher)
- Travel, conversion and speed–time graphs: gradient as a rate of change
How it works
Learn
12 lessons, each labelled with its IGCSE 0580 and GCSE references.
Practise
Six stations, six fresh questions each visit, with hints that fade.
Challenge
Mixed questions from every station with a skill-by-skill report.
For teachers
Open Teacher options to choose Core / Foundation or Extended / Higher. Nothing is uploaded: progress stays in each student's browser, so no accounts or data-protection paperwork are needed.
Which exams it covers
Straight-line graphs appear on almost every paper. Perpendicular lines and ax + by = c are IGCSE Extended; perpendicular lines are GCSE Higher.
| Topic | GCSE (AQA, Edexcel) | Cambridge IGCSE 0580 |
|---|---|---|
| Drawing straight-line graphs from a table of values | A9 | C3.2 / E3.2 |
| Gradient from a grid | A10 | C3.3 / E3.3 |
| Gradient from the coordinates of two points | A10 | E3.3 (Core: from a grid only) |
| y = mx + c: gradient, y-intercept, equation from a graph or two points | A9, A10 | C3.5 / E3.5 |
| Equations in the form ax + by = c | A9 | E3.5 (Extended) |
| Parallel lines | A9 | C3.6 / E3.6 |
| Perpendicular lines and the perpendicular bisector | A9 (Higher) | E3.7 (Extended only) |
| Gradient as a rate of change: travel and conversion graphs | R14, A14 | C2.9 / E2.9 |
| Speed–time graphs: acceleration and distance | A15 (Higher) | E2.9 (Extended) |
Worked examples
Four examples in the style of recent IGCSE and GCSE papers.
Gradient and intercept · Extended
Find the gradient and y-intercept of the line 5x + 4y = 8.
- 4y = −5x + 8
- y = −5/4x + 2
Answer: gradient −5/4, y-intercept 2
Parallel lines
Find the equation of the line parallel to y = 4x − 1 that passes through (1, −3).
- Parallel lines have the same gradient: m = 4
- Substitute (1, −3): −3 = 4 × 1 + c, so c = −7
Answer: y = 4x − 7
Perpendicular bisector · Extended / Higher
Find the equation of the perpendicular bisector of the line joining (−3, 8) and (9, −2).
- Midpoint = (3, 3)
- Gradient of the line = −10 ÷ 12 = −5/6, so the perpendicular gradient is 6/5
- 3 = 6/5 × 3 + c, so c = −3/5
Answer: y = 6/5x − 3/5 (or 5y = 6x − 3)
Common mistakes the game targets
- Putting the run on top. Gradient is rise ÷ run: the change in y goes on top.
- Mixing the order of the points. Subtract in the same order top and bottom: (y₂ − y₁) ÷ (x₂ − x₁).
- Calling a horizontal line “undefined”. A horizontal line has gradient 0. A vertical line's gradient cannot be calculated.
- Reading m before rearranging. Rearrange into y = mx + c first. In 2y = 6x + 4 the gradient is 3, not 6.
- Only flipping for a perpendicular gradient. Flip the fraction and change the sign: 2 becomes −1/2.
- Forgetting the midpoint in a perpendicular bisector. The bisector passes through the midpoint of AB, not through A or B.
Questions teachers and parents ask
Is the game free?
Yes. It is free to use, with no account, no adverts and no tracking.
Which exams does it suit?
Cambridge IGCSE 0580 Core and Extended, and GCSE Foundation and Higher (AQA and Edexcel). Every lesson shows its IGCSE and GCSE references.
Can students type equations?
Yes. Any correct form is accepted, such as y = 2x − 3 or 2x − y = 3, and fractions like −3/4.
Does it work on phones?
Yes. It works on phones, tablets, laptops and Chromebooks.
Can students print their results?
Yes. The Challenge ends with a skill report and a Print report button.
Matching worksheet packs
Printable practice and exam-style tests on the same topic, with full worked solutions.
Graphs
Graphs: y = mx + c and Gradients (AQA 8300)
Exam-style practice questions for Foundation and Higher tiers, with complete solutions.
Free practice: Gradient City
Graphs
Graphs — IGCSE 0580 Paper 2
Paper 2 (non-calculator) style practice and an exam-style test.
Free practice: Gradient City
Graphs
Graphs — IGCSE 0580 Paper 4
Paper 4 (calculator) style practice and an exam-style test.
Free practice: Gradient City
Need worksheets and lessons to go with the games?
Printable IGCSE and GCSE resources from Mathwright: worksheets, exam-style practice and full worked solutions.
More coordinate geometry games
Coordinates & the four quadrants
Coordinate Treasure Map
Travel from Base Camp to the Treasure Chest by reading, plotting and moving between coordinates in all four quadrants.
Midpoint & length of a line segment
Coordinate Rescue Mission
Six stations on the midpoint and length of a line segment, missing points, exact surd lengths and dividing a line, with past-paper question types.
Translations, reflections, rotations & enlargements
Transformation Station
Draw the image on the grid and describe fully the single transformation, exactly as on IGCSE 0580 and GCSE papers.