Target Mathematics

1.19: Graphical and algebraic inequalities

4PM1/1/January/2015 — Question 5 · 9 marks

1.19 diagram 1
(a) On the axes opposite, draw the lines with equations
(i) y=−x−1y=-x-1
(ii) y=3x−9y=3x-9
(iii) 2y=x+72y=x+7 (4)
(b) Show, by shading, the region RR defined by the inequalities
y≥−x−1,y≥3x−9,2y≤x+7y\ge -x-1,\qquad y\ge3x-9,\qquad 2y\le x+7
(1)
For all points in RR with coordinates (x,y)(x,y), P=y−2xP=y-2x.
(c) Find
(i) the greatest value of PP,
(ii) the least value of PP. (4)