1.5: Past-paper question 4

4PM1/2/November/2023 — Question 4 · 8 marks

1.5 diagram 1
(a) On the axes opposite, draw the line with equation
(i) y=−x−1(ii) y=−3x+8=0(iii) 2y=x+8\begin{aligned} \text{(i) } y &= -x - 1 & \text{(ii) } y &= -3x + 8 = 0 & \text{(iii) } 2y &= x + 8 \\ & & & &\end{aligned}
(3)
(b) Show, by shading on your graph, the region R\displaystyle R defined by the inequalities
y≥−x−1andy≥3x−8and2y≤x+8y \geq -x - 1 \quad \mathrm{and} \quad y \geq 3x - 8 \quad \mathrm{and} \quad 2y \leq x + 8
(1)
For all points in R\displaystyle R, with coordinates (x,y)\displaystyle (x, y)
P=2y−3xP = 2y - 3x
(c) Find
(i) the greatest value of P\displaystyle P
(ii) the least value of P\displaystyle P
(4)
Only use this grid if you need to redraw your graph.