Moderate -0.8 This is a straightforward coordinate geometry question requiring students to find the gradient of the line through two points, write its equation, and show the lines are parallel (same gradient). It's simpler than average as it only requires basic techniques with no problem-solving insight, though the 'show that' format requires clear working.
(Gradient of line segment) \(= \frac{5-(-4)}{-1-2} = -3\)
M1
AO3.1a — Attempt to find gradient; accept sign errors but not reciprocal
Given line \(y = -3x + 10\) has gradient \(-3\); same gradient so parallel lines
M1
AO1.1a — Finding gradient of given line
Neither point lies on the line so the lines do not intersect
A1
AO2.2a — Must conclude based on lines being parallel and not the same line
[3]
Alternative solution:
Answer
Marks
Guidance
Answer/Working
Marks
Guidance
Gradient \(= \frac{5-(-4)}{-1-2} = -3\)
M1
Attempt to find gradient; accept sign errors but not reciprocal
Equation of line: \(y-(-4) = -3(x-2)\), giving \(y = -3x+2\)
M1
Finding equation of given line
Given line is \(y = -3x+10\) which is parallel, so lines do not intersect
A1
Conclusion referring to parallel lines. Allow for solving two lines simultaneously and stating there are no solutions.
## Question 2:
| Answer/Working | Marks | Guidance |
|---|---|---|
| (Gradient of line segment) $= \frac{5-(-4)}{-1-2} = -3$ | M1 | AO3.1a — Attempt to find gradient; accept sign errors but not reciprocal |
| Given line $y = -3x + 10$ has gradient $-3$; same gradient so parallel lines | M1 | AO1.1a — Finding gradient of given line |
| Neither point lies on the line so the lines do not intersect | A1 | AO2.2a — Must conclude based on lines being parallel and not the same line |
| **[3]** | | |
**Alternative solution:**
| Answer/Working | Marks | Guidance |
|---|---|---|
| Gradient $= \frac{5-(-4)}{-1-2} = -3$ | M1 | Attempt to find gradient; accept sign errors but not reciprocal |
| Equation of line: $y-(-4) = -3(x-2)$, giving $y = -3x+2$ | M1 | Finding equation of given line |
| Given line is $y = -3x+10$ which is parallel, so lines do not intersect | A1 | Conclusion referring to parallel lines. Allow for solving two lines simultaneously and stating there are no solutions. |
2 Show that the line which passes through the points $( 2 , - 4 )$ and $( - 1,5 )$ does not intersect the line $3 x + y = 10$.
\hfill \mbox{\textit{OCR MEI Paper 1 2019 Q2 [3]}}