(a) On the grid, draw the graph of \(y = 2x + 3\) for values of \(x\) from −2 to 3(3)
(b) Show, by shading on the grid, the region that satisfies all three of the inequalities\[x \leqslant 2 \qquad y \geqslant 1 \qquad y \leqslant 2x + 3\]Label the region R. (2)
Mark scheme (a)
Scheme
Marks
\(x\)
−2
−1
0
1
2
3
\(y\)
−1
1
3
5
7
9
B3
B2
B1
(3)
Notes
B3: For a correct line between \(x = -2\) and \(x = 3\)
B2: For a correct straight line segment through at least 3 of (−2, −1) (−1, 1) (0, 3) (1, 5) (2, 7) (3, 9) OR for all of (−2, −1) (−1, 1) (0, 3) (1, 5) (2, 7) (3, 9) plotted but not joined
B1: For at least 2 correct points plotted or stated (ignore incorrect points) OR for a line drawn with a positive gradient through (0, 3) and clear intention to use a gradient of 2 (eg. a line through (0, 3) and (0.5, 5) OR a line drawn with a gradient of 2
Mark scheme (b)
Scheme
Marks
M1
A1
(2)
(5 marks)
Notes
M1: for \(x = 2\) and \(y = 1\) drawn
A1: for correct region identified
NB: Region may be unshaded or shaded, condone missing label
