Modulus Function - Graphs of Modulus Function

The diagram shows the graph of \(y=\left| k-2x \right|+m\), where \(k\) and \(m\) are integers. \(A\) is the point where the graph intersects the \(y\)-axis, and \(B\)and \(C\)are the points where it intersects the \(x\)-axis. Point \(D\left( 3,-2 \right)\) is the vertex of the graph.

1. Find the value of \(k\) and of \(m\).
2. Hence find the coordinates of \(A\), \(B\)and \(C\).
3. Using the graph, write down the range of values of \(p\), such that the equation \(px=\left| k-2x \right|+m\) has 2 distinct solutions.