Target Mathematics

1.18: Graphical and algebraic inequalities

4PM1/1/January/2018 — Question 2 · 8 marks

1.18 diagram 1
(a) On the grid opposite, draw
(i) the line with equation y=3x−3y=3x-3
(ii) the line with equation 3x+2y=123x+2y=12 (2)
(b) Show, by shading, the region RR defined by the inequalities
y≤3x−33x+2y≤12y≥−1y\le 3x-3 \qquad 3x+2y\le12 \qquad y\ge-1
(2)
For all points in RR with coordinates (x,y)(x,y)
P=4x−yP=4x-y
(c) Find the greatest value of PP. (4)