22 The straight line L has gradient 5 and passes through the point with coordinates \((0, -3)\)
(a) Write down an equation for L. (2)
(b)The region R, shown shaded in the diagram, is bounded by four straight lines. Write down the inequalities that define R. (2)
Mark scheme (a)
Scheme
Marks
\(y = 5x - 3\) oe
B2
(2)
Notes
B2: fully correct equation eg \(y = 5x + -3\) or \(y - -3 = 5(x - 0)\) If not B2 then B1 for \(y = 5x\) or \(y = 5x + a\) or \(y = bx - 3\) (\(b \ne 0\)) or (\(L =\)) \(5x - 3\)
Mark scheme (b)
Scheme
Marks
\(x \geqslant 0\), \(x \leqslant 2\), \(y \geqslant 1\), \(y \leqslant 3\) or Answer: \(0 \leqslant x \leqslant 2\) \(1 \leqslant y \leqslant 3\)
B2
(2)
(4 marks)
Notes
B2: fully correct oe (B1 for 2 or 3 out of 4 inequalities correct) (Treat double-ended inequalities as two separate inequalities) (SC B2 \(y \gt 3\), \(y \lt 1\), \(x \lt 0\), \(x \gt 2\)) Accept <, ≤, > and ≥ throughout
