A log graph translates to what shape on log scales?

When a relationship is plotted on a log-log scale, it transforms any power law relationship into a linear representation. This means that if the original data reflects variation, the plotted graph will appear as a straight line rather than a curve. The slope of this line corresponds to the exponent of the power law relationship. Therefore, a straight line with a non-zero slope is indicative of a relationship where the variables involved are related by a power function, demonstrating that there is indeed variation in the data.

In contrast, if the variation were to be absent, the graph would show a flat line, signifying no change irrespective of the values on the axes. Additionally, if there were a relationship involving exponential growth, it would not appear as a straight line on a log-log plot, but rather as a curve that implies a differing type of relationship than a linear association. Thus, the chosen answer accurately reflects the behavior of data on log scales when variation is present.