1.3: Past-paper question 5

4PM1/2/June/2023 — Question 5 · 7 marks

1.3 diagram 1
(a) On the grid opposite draw the line with equation
(i)y=2x+5(ii)4y=x−8(iii)5y+3x=30(i) \quad y = 2x + 5 \quad (ii) \quad 4y = x - 8 \quad (iii) \quad 5y + 3x = 30
(3)
(b) Show, by shading, the region R\displaystyle R defined by the inequalities
y≤2x+54y≥x−85y+3x≤30y \leq 2x + 5 \quad 4y \geq x - 8 \quad 5y + 3x \leq 30
(1)
For all points in R\displaystyle R with coordinates (x,y)\displaystyle (x, y)
P=2x−5yP = 2x - 5y
(c) Using your graph, find the least value of P\displaystyle P
(3)
Only use this grid if you need to redraw your graph.