1.2: Sketch lines and shade a region

4PM1/1/November/2020 — Question 2 · 4 marks

(a) Using the axes below, sketch the lines with equations
(i) y=6\displaystyle y=6,
(ii) y+x=10\displaystyle y+x=10,
(iii) y=2x−5\displaystyle y=2x-5.
Show the coordinates of any point where each line crosses the coordinate axes.
(3)
(b) Show, by shading on your sketch, the region R\displaystyle R defined by the inequalities
y≤6,y+x≤10,y≥2x−5,x≥0.y\leq6, \qquad y+x\leq10, \qquad y\geq2x-5, \qquad x\geq0.
(1)