中文（繁體）
中文（简体）
English
S3 Maths: Equations of Straight Lines (Paper 4 (error clinic))
S3 Maths: Equations of Straight Lines (Paper 4 (error clinic))
Paper 4 (error clinic): ten straight-line questions with answers and one-line notes.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S3 Maths: Equations of Straight Lines |
| Level | S3 |
02 Questions (10 items)
- FoundationFind the slope of the line through (2, 1) and (6, 9).
- FoundationFind the x-intercept of y = -3x + 4.
- FoundationFind the line through (5, 2) with slope -1.
- IntermediateDoes (3, 8) lie on y = 2x + 2?
- IntermediateWrite the equation of the line parallel to the x-axis through (0, -5).
- IntermediateA line has slope 3. What is the slope of a line perpendicular to it?
- ChallengeFind the equation of the line through (-2, -3) and (2, 5).
- ChallengeFind the intersection of y = 3x – 4 and y = -x + 8.
- ChallengeFind the slope of 5x + 2y – 10 = 0.
- Error redoA student writes that a line with slope 2 and y-intercept 3 is y = 3x + 2. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Slope = 2 | The change in y is 8 and the change in x is 4, so the slope is 8 over 4, which is 2. |
| 2 | x = 4/3 | Set y = 0 to get -3x + 4 = 0, so 3x = 4 and x = 4/3. |
| 3 | y = -x + 7 | Write y = -x + c and substitute (5, 2) to get 2 = -5 + c, so c = 7. |
| 4 | Yes, because 2 times 3 plus 2 equals 8 | Substituting x = 3 gives 8, which matches the y value of the point. |
| 5 | y = -5 | A line parallel to the x-axis is horizontal with slope 0, so every point has y value -5. |
| 6 | -1/3 | The perpendicular slope is the negative reciprocal, so the negative reciprocal of 3 is -1/3. |
| 7 | y = 2x + 1 | The slope is 8 over 4, which is 2, and substituting (2, 5) gives 5 = 4 + c, so c = 1. |
| 8 | (3, 5) | Setting the two expressions equal gives 4x = 12, so x = 3 and y = 5. |
| 9 | Slope = -5/2 | Rearranging gives 2y = -5x + 10, so y = -(5/2)x + 5 and the slope is -5/2. |
| 10 | The slope and intercept are swapped; it should be y = 2x + 3 | In y = mx + c the coefficient of x is the slope and the constant is the y-intercept, so the two cannot be swapped. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Start every straight-line question by writing down what you are given: two points, a point with a slope, or an equation. For slope from two points, subtract the y values and the x values in the same order, because swapping the order flips the sign. Once you have the slope, use y = mx + c and substitute the known point to find c. To convert Ax + By + C = 0 into slope-intercept form, isolate y so the slope is -A/B. Parallel lines share the same slope, perpendicular slopes multiply to -1, and that pair of facts settles most reasoning questions. Finish by substituting your answer back and checking that the intercepts match the graph.Tutor Registration →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.
© TutorZone · www.tutorzone.com.hk · For personal study and teaching use only.