Two possible ways to sketch the graph are here.

One way is to do a step by step transformation of the graph.

1. We start from the basic graph of y = x.
2. We then draw y = -x, since the equation to consider is y = |11 - 3x|.
3. We then draw y = -3x, which will be steeper than the line y = -x.
4. We then draw y = 11 - 3x, which is the same graph shifted upwards.
5. We then apply modulus, which will reflect any portion below the x-axis upwards above the x-axis.

The other way is very similar in approach to the sketching of a quadratic graph in which the equation is already in completed square form.

1. We first locate the "turning point" by setting the term in the modulus to zero. This is analogous to quadratic expressions, where we locate the turning point by setting the term in brackets to zero.

2. We then determine whether the graph will be "smiley face" or "sad face". This depends on the signage outside the modulus sign. If there is a negative sign, then the modulus graph is "sad face". Otherwise, it is a "smiley face". This is analogous to the quadratic case where the shape depends on the signage of the term in x2.

3. We then draw the graph, noting the shape and the location of the turning point.