Intermediate November 2022 Unit 1 Q18
18. The diagram below shows the graph of a straight line for values of \(x\) from –1 to 3.
(a)
(i) Write down the gradient of the line above. [1]
(ii) Write down the equation of the line in the form \(y = mx + c\). [2]
(b) Show that the lines\[y = 3x - 8 \quad \text{and} \quad 2y - 6x = 23\]are parallel to each other. [2]
| Scheme | Marks | Comments |
|---|---|---|
| (i) 4 | B1 | Accept 4/1 or equivalent. The correct gradient has to be unambiguously shown. \(y = 4x - 2\) is B0, but \(y =\)4\(x - 2\) is B1. Award B0 for a final answer of \(4x\). |
| (ii) \(y = 4x - 2\) | B2 | FT ‘their gradient’ from (a) Award B1 for one of the following:
|
| Scheme | Marks | Comments |
|---|---|---|
| Valid explanation with rearranged equation AND indicating that the gradient is 3 or equivalent e.g. “2y - 6\(x\) = 23 is the same as \(y\) = 3\(x\) + 11·5, so the gradient of both lines is 3” “2\(y\) = 6\(x\) + 23 and 2\(y\) = 6\(x\) – 16 and the gradient of both lines is 3”. | B2 | B1 for one of the following:
Do not allow:
|