(a)[2]
On the grid, shade region $R$, defined by the inequalities $1\le x\le5$, $2\le y\le4$.
(b(i))[1]
Draw the line $y=\frac{1}{3}x+k$ so that it goes through a point in $R$ for which $k$ is as great as it can be.
(b(ii))[1]
State the greatest value of $k$.