Foundation November 2023 Paper 2 Q29
29 A straight line passes through (3, 14) and (12, 32)
Work out the equation of the line.
Give your answer in the form \(\quad y = mx + c\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(\dfrac{32 - 14}{12 - 3}\) or \(\dfrac{18}{9}\) or \((m =)\ 2\) | M1 | oe eg \(\dfrac{14 - 32}{3 - 12}\) implied by \(y = 2x \ldots\) |
| \(14 =\) their \(2 \times 3 + c\) or \(32 =\) their \(2 \times 12 + c\) or \((m =)\ 2\) and \(c = 8\) or \(y - 14 =\) their \(2(x - 3)\) or \(y - 32 =\) their \(2(x - 12)\) | M1dep | oe |
| \(y = 2x + 8\) | A1 | |
| Alternative method 2 | ||
| \(14 = 3m + c\) and \(32 = 12m + c\) and \(32 - 14 = 12m - 3m\) or \(m = 2\) or \(56 = 12m + 4c\) and \(32 = 12m + c\) and \(56 - 32 = 4c - c\) or \(c = 8\) | M1 | oe correct method to work out \(m\) or \(c\) using simultaneous equations implied by \(y = 2x \ldots\) or \(y = mx + 8\) |
| Correct substitution of their \(m\) into one of the original equations or correct substitution of their \(c\) into one of the original equations or \(m = 2\) and \(c = 8\) | M1dep | |
| \(y = 2x + 8\) | A1 | |