Final answer:
The slope of a line when y varies directly with x is the proportionality constant k, representing the constant rate of change between y and x.
Step-by-step explanation:
When y varies directly with x, it means that the two are directly proportional to each other. In mathematical terms, the relationship can be represented by the equation y = kx, where k is the proportionality constant. When plotting this relationship on a graph with y as the dependent variable and x as the independent variable, we would get a straight line that passes through the origin (0, 0).
The slope of a line in a graph showing a direct variation represents how much y changes for each unit change in x. The slope is a constant value for any straight line, and in the context of directly proportional variables, the slope is the constant k. Therefore, when y varies directly with x, the slope of the graph of that relationship is k, which is the proportionality constant.