| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2017 |
| Session | October |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Parallel line through point |
| Difficulty | Easy -1.2 This is a straightforward two-part question testing basic coordinate geometry: rearranging a linear equation to find gradient, then using the parallel line condition (same gradient) and point-substitution to find a new equation. Both parts are routine textbook exercises requiring only standard algebraic manipulation with no problem-solving insight needed. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Gradient \(= -4\) | B1 | Final answer. Do not allow \(-\frac{8}{2}\) or \(-\frac{4}{1}\) or \(-4 \to \frac{1}{4}\). Do not allow if left as \(y = -4x + ..\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Gradient of parallel line equals their previous gradient | M1 | May be implied by sight of \('-4'\) in a gradient equation |
| \(y - 16 = {-4}(x-(-\frac{3}{4}))\) | M1 | Attempt to find equation using \((-\frac{3}{4}, 16)\) and a numerical gradient. Condone sign error on one bracket. If \(y=mx+c\) used must proceed to finding \(c\) |
| \(y = -4x + 13\) | A1 | cao. Allow \(m=-4, c=13\) |
## Question 1:
**(a)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Gradient $= -4$ | B1 | Final answer. Do not allow $-\frac{8}{2}$ or $-\frac{4}{1}$ or $-4 \to \frac{1}{4}$. Do not allow if left as $y = -4x + ..$ |
**(b)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Gradient of parallel line equals their previous gradient | M1 | May be implied by sight of $'-4'$ in a gradient equation |
| $y - 16 = {-4}(x-(-\frac{3}{4}))$ | M1 | Attempt to find equation using $(-\frac{3}{4}, 16)$ and a numerical gradient. Condone sign error on one bracket. If $y=mx+c$ used must proceed to finding $c$ |
| $y = -4x + 13$ | A1 | cao. Allow $m=-4, c=13$ |
---\begin{enumerate}
\item The line $l _ { 1 }$ has equation
\end{enumerate}
$$8 x + 2 y - 15 = 0$$
(a) Find the gradient of $l _ { 1 }$
The line $l _ { 2 }$ is parallel to the line $l _ { 1 }$ and passes through the point $\left( - \frac { 3 } { 4 } , 16 \right)$.\\
(b) Find the equation of $l _ { 2 }$ in the form $y = m x + c$, where $m$ and $c$ are constants.
\hfill \mbox{\textit{Edexcel C12 2017 Q1 [4]}}