1.8: Past-paper question 4

4PM1/1/June/2025 — Question 4 · 8 marks

1.8 diagram 1
(a) On the grid opposite, draw the graph of the line with equation
(i)3x+2y=18(ii)x+3y6=0(iii)y=3x(i) \quad 3x + 2y = 18 \quad (ii) \quad x + 3y - 6 = 0 \quad (iii) \quad y = 3x
(3)
(b) Show, by shading on the grid, the region R\displaystyle R defined by the inequalities
3x+2y18x+3y60y3x3x + 2y \leq 18 \quad x + 3y - 6 \geq 0 \quad y \leq 3x
(1)
For all points in R\displaystyle R, with coordinates (x,y)\displaystyle (x, y)
P=2xyP = 2x - y
(c) find the least value of P\displaystyle P
(4)
Only use this grid if you need to redraw your graph.