Target Mathematics

1.17: Graphical and algebraic inequalities

4PM1/2/June/2017 — Question 1 · 5 marks

1.17 diagram 1
(a) On the grid opposite, draw the graphs of the lines with equations
(i) y=2xy=2x\qquad (ii) y=6−xy=6-x\qquad (iii) 2y=x−22y=x-2 (3)
(b) Show, by shading on the grid, the region RR defined by the inequalities
y≤2x,y≤6−x,2y≥x−2,y≥0y\le2x,\qquad y\le6-x,\qquad 2y\ge x-2,\qquad y\ge0
(1)
For all points in RR, with coordinates (x,y)(x,y),
P=y+2xP=y+2x
(c) Find the greatest value of PP. (1)