Free Gradient & equation of a line questions for IGCSE Mathematics (0580), part of Coordinate geometry. Each question has the answer and the marking points an examiner would look for.
Generate a full Gradient & Equation of a Line worksheet →All Coordinate geometry questionsThe line L has gradient 2 and passes through the point (2, 9).
L crosses the x-axis at A and the y-axis at B. O is the origin.
Find the area of triangle OAB.
| Part | Answer and marking points | Marks |
|---|---|---|
| 254 y = 2x + 5 M1 B = (0, 5), A = (−52, 0) A1 ½ × base × height M1 254 A1 | 4 |
The line L has equation y = 2x.
A is the point (1, 7) and B is the point (3, 9). A and B are on the same side of L.
Find the coordinates of the point on L that is nearest to A, and the exact shortest distance from A to L.
P is a point on L. Find the coordinates of P for which AP + PB is as small as possible, and the exact value of this least distance.
Q is a point on L. Find the coordinates of Q for which QA − QB is as large as possible, and the exact value of this greatest difference.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | (3, 6); √5 line through A perpendicular to L: y − 7 = −½(x − 1) M1 meets y = 2x at (3, 6) A1 √(22 + 12) = √5 A1 | 3 |
| (b) | P = (3.75, 7.5); least AP + PB = 2√5 reflects A in L: A′ = (5, 5) M1 A′ = 2(3, 6) − (1, 7) A1 least AP + PB is when P is on A′B: y = −2x + 15 M1 P = (3.75, 7.5) A1 A′B = √(22 + 42) = 2√5 A1 | 5 |
| (c) | Q = (6, 12); 2√2 QA − QB ≤ AB, with equality when Q, B, A are collinear: line AB is y = x + 6 M1 Q = (6, 12) A1 AB = 2√2 A1 | 3 |
The equation of a line is 3x + 6y = 36.
Find the gradient of the line.
Find the coordinates of the points where the line crosses the x-axis and the y-axis.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | −12 rearranges to y = … M1 −12 A1 | 2 |
| (b) | (12, 0) and (0, 6) (12, 0) B1 (0, 6) B1 | 2 |
The diagram shows the line L.
Find the gradient of line L.
Find the equation of line L in the form y = mx + c.
Find the equation of the line parallel to L that passes through the point (−6, 3).
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | −12 −48 using two points on the line M1 −12 A1 | 2 |
| (b) | y = −12x − 1 y = −12x − 1 B2 B1 for correct gradient or correct intercept in y = mx + c | 2 |
| (c) | y = −12x 3 = −12 × −6 + c M1 y = −12x A1 | 2 |
The line L has gradient −1 and passes through the point (2, −5).
L crosses the x-axis at A and the y-axis at B. O is the origin.
Find the area of triangle OAB.
| Part | Answer and marking points | Marks |
|---|---|---|
| 92 y = −x − 3 M1 B = (0, −3), A = (−3, 0) A1 ½ × base × height M1 92 A1 | 4 |
The equation of a line is 2x + 3y = 12.
Find the gradient of the line.
Find the coordinates of the points where the line crosses the x-axis and the y-axis.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | −23 rearranges to y = … M1 −23 A1 | 2 |
| (b) | (6, 0) and (0, 4) (6, 0) B1 (0, 4) B1 | 2 |
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Meet Riyaz →Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in