Sketch, on the same diagram, the graphs of \(y = | x + 2 k |\) and \(y = | 2 x - 3 k |\), where \(k\) is a positive constant.
Give, in terms of \(k\), the coordinates of the points where each graph meets the axes.
Find, in terms of \(k\), the coordinates of each of the two points where the graphs intersect.
Find, in terms of \(k\), the largest value of \(t\) satisfying the inequality
$$\left| 2 ^ { t } + 2 k \right| \geqslant \left| 2 ^ { t + 1 } - 3 k \right| .$$