The constant of proportionality in the equation \(y = 32x\) is 32. This means that for every unit increase in \(x\), \(y\) increases by 32 units.
In terms of the graph of a proportional relationship, the characteristic it displays is that it will pass through the point (0, 0). This is because a proportional relationship is defined by the ratio of \(y\) to \(x\) being constant, which leads to the origin being a point on the graph.