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S3 Maths: Equations of Straight Lines (Paper 2 (intermediate))
S3 Maths: Equations of Straight Lines (Paper 2 (intermediate))
Paper 2 (intermediate): 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(-2, 5) and B(4, -7).
- FoundationFind the line through (3, -1) that is parallel to y = 2x + 7.
- FoundationFind the line through (4, 3) perpendicular to a line of slope 1/2.
- IntermediateFind the equation of the line through (2, 5) and (6, 5).
- IntermediateGive the slope and both intercepts of 3x + 4y = 12.
- IntermediateFind the equation of the line through (-1, 2) and (3, 10).
- ChallengeFind the intersection of y = x + 1 and y = -2x + 10.
- ChallengeFind the midpoint of A(1, 3) and B(5, 9) and the slope of AB.
- ChallengeIs (4, 11) on the line through (1, 2) and (3, 8)?
- Error redoFind the general form of the line through (0, -3) with slope 2/3.
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Slope = -2 | The change in y is -7 minus 5, which is -12, and the change in x is 4 minus -2, which is 6, so the slope is -2. |
| 2 | y = 2x – 7 | Parallel lines share slope 2, so write y = 2x + c and substitute (3, -1) to get -1 = 6 + c, giving c = -7. |
| 3 | y = -2x + 11 | The perpendicular slope is the negative reciprocal of 1/2, which is -2, and substituting (4, 3) gives 3 = -8 + c, so c = 11. |
| 4 | y = 5 | Both points share the same y value, so the slope is 0 and the line is horizontal at y = 5. |
| 5 | Slope -3/4, y-intercept 3, x-intercept 4 | Rearranging gives y = -(3/4)x + 3, and setting y = 0 gives 3x = 12, so the x-intercept is 4. |
| 6 | y = 2x + 4 | The slope is 10 minus 2 over 3 minus -1, which is 2, and substituting (-1, 2) gives 2 = -2 + c, so c = 4. |
| 7 | (3, 4) | Set x + 1 equal to -2x + 10, so 3x = 9 gives x = 3 and substituting back gives y = 4. |
| 8 | Midpoint (3, 6), slope 3/2 | The midpoint averages the coordinates, and the slope is 9 minus 3 over 5 minus 1, which is 6 over 4, that is 3/2. |
| 9 | Yes | The slope is 6 over 2, which is 3, so the line is y = 3x – 1, and at x = 4 the value is 11, matching the point. |
| 10 | 2x – 3y – 9 = 0 | Start from y = (2/3)x – 3, multiply by 3 to get 3y = 2x – 9, then rearrange into 2x – 3y – 9 = 0. |
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 →
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