中文（繁體）
中文（简体）
English
S3 Maths: Equations of Straight Lines (Paper 1 (basics))
S3 Maths: Equations of Straight Lines (Paper 1 (basics))
Paper 1 (basics): 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 A(1, 2) and B(4, 8).
- FoundationA line has slope 3 and y-intercept -2. Write its equation.
- FoundationState the slope and y-intercept of y = 2x + 5.
- IntermediateA line passes through (2, 3) with slope 4. Find its equation.
- IntermediateFind the equation of the line through (0, 4) and (3, 1).
- IntermediateFind the x-intercept of y = 3x – 12.
- ChallengeDoes the point (2, 7) lie on the line y = 3x + 1?
- ChallengeWrite the equation of the horizontal line through (5, -3).
- ChallengeWrite the equation of the vertical line through (-2, 6).
- Error redoGive the slope, y-intercept and x-intercept of y = -2x + 6.
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Slope = 2 | The change in y is 8 minus 2, which is 6, and the change in x is 4 minus 1, which is 3, so 6 over 3 gives 2. |
| 2 | y = 3x – 2 | The slope-intercept form is y = mx + c, so putting m as 3 and c as -2 gives y = 3x – 2. |
| 3 | Slope 2, y-intercept 5 | The equation is already in y = mx + c form, so the coefficient of x is the slope and the constant is the y-intercept. |
| 4 | y = 4x – 5 | Write y = 4x + c, substitute x = 2 and y = 3 to get 3 = 8 + c, so c is -5. |
| 5 | y = -x + 4 | The slope is 1 minus 4 over 3 minus 0, which is -1, and at x = 0 the y value is already 4. |
| 6 | x = 4 | Set y = 0 for the x-intercept, so 3x – 12 = 0 gives x = 4. |
| 7 | Yes, because 3 times 2 plus 1 equals 7 | Substituting x = 2 gives 7, which matches the y value of the point, so the point is on the line. |
| 8 | y = -3 | Every point on a horizontal line has the same y value, so the equation is y equals that value. |
| 9 | x = -2 | Every point on a vertical line has the same x value, the slope is undefined, and the equation is x equals a constant. |
| 10 | Slope -2, y-intercept 6, x-intercept 3 | The slope and y-intercept come straight from the slope-intercept form, and setting y = 0 in -2x + 6 = 0 gives x = 3. |
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.