Easy -1.2 This is a straightforward coordinate geometry question requiring two standard procedures: finding the perpendicular gradient (negative reciprocal of -2/3 gives 3/2) and using point-slope form to find the equation. It's routine AS-level material with no problem-solving element, making it easier than average but not trivial since it requires careful algebraic manipulation.
6 Determine the equation of the line which passes through the point \(( 4 , - 1 )\) and is perpendicular to the line with equation \(2 x + 3 y = 6\).
Give your answer in the form \(y = m x + c\), where \(m\) is a fraction in its lowest terms and \(c\) is an integer.
May be implied by a correct re-arrangement of given equation or by the correct perp gradient, or by the calculation of \(m_2\). Condone \(m_1 = -\frac{2}{3}x\)
\(m_2 = -\frac{1}{their -\frac{2}{3}}\)
M1
Must follow legitimate attempt to find gradient of perp line. Condone \(m_2 = \frac{3}{2}x\) etc if \(\frac{3}{2}\) used in their perp. line
\(y - -1 = \frac{3}{2}(x-4)\) oe
M1
May see e.g. \(-1 = \frac{3}{2} \times 4 + c\). This mark is for using the equation of the line correctly with the point \((4,-1)\) so can be scored even with an incorrect gradient provided their \(m_2 \neq their\ m_1\)
\(y = \frac{3}{2}x - 7\)
A1
Must be in this form only.
## Question 6:
| Answer | Mark | Guidance |
|--------|------|----------|
| $m_1 = -\frac{2}{3}$ | B1 | May be implied by a correct re-arrangement of given equation or by the correct perp gradient, or by the calculation of $m_2$. Condone $m_1 = -\frac{2}{3}x$ |
| $m_2 = -\frac{1}{their -\frac{2}{3}}$ | M1 | Must follow legitimate attempt to find gradient of perp line. Condone $m_2 = \frac{3}{2}x$ etc if $\frac{3}{2}$ used in their perp. line |
| $y - -1 = \frac{3}{2}(x-4)$ oe | M1 | May see e.g. $-1 = \frac{3}{2} \times 4 + c$. This mark is for using the equation of the line correctly with the point $(4,-1)$ so can be scored even with an incorrect gradient provided their $m_2 \neq their\ m_1$ |
| $y = \frac{3}{2}x - 7$ | A1 | Must be in this form only. |
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6 Determine the equation of the line which passes through the point $( 4 , - 1 )$ and is perpendicular to the line with equation $2 x + 3 y = 6$.
Give your answer in the form $y = m x + c$, where $m$ is a fraction in its lowest terms and $c$ is an integer.
\hfill \mbox{\textit{OCR MEI AS Paper 2 2024 Q6 [4]}}