Moderate -0.8 This is a straightforward coordinate geometry question requiring students to find the gradient of a line from two points and compare it to the gradient of a line in standard form. It involves routine algebraic manipulation and basic understanding of parallel lines (equal gradients), making it easier than average but not trivial due to the need to rearrange the equation and perform accurate calculations.
Determine whether the line with equation \(2x + 3y + 4 = 0\) is parallel to the line through the points with coordinates \((9, 4)\) and \((3, 8)\).
[4 marks]
Question 7:
7 | Explains that equal gradients
implies that lines are parallel | AO2.4 | E1 | Parallel lines have equal gradient
2 4
2x + 3y + 4 = 0 y = x
3 3
2
So gradient is
3
Gradient of line through (9, 4) and
84 2
(3, 8) is =
39 3
So line with equation 2x + 3y + 4 = 0 is
parallel to the line joining the points with
coordinates (9, 4) and (3, 8) as both
2
have gradient
3
Finds the gradient of the given line
CAO | AO1.1b | B1
Finds the gradient of the line
through the 2 given points
CAO | AO1.1b | B1
Deduces that the two lines are
parallel | AO2.2a | R1
Total | 4
Q | Marking Instructions | AO | Marks | Typical Solution
Determine whether the line with equation $2x + 3y + 4 = 0$ is parallel to the line through the points with coordinates $(9, 4)$ and $(3, 8)$.
[4 marks]
\hfill \mbox{\textit{AQA AS Paper 1 Q7 [4]}}