Which graphical representation is appropriate to use when comparing a changing variable with an unchanging value?

A bar graph is the appropriate choice for comparing a changing variable with an unchanging value because it effectively represents discrete data and allows for clear visual comparisons between different groups or categories. In this context, the changing variable can be plotted along one axis (typically the vertical axis), while the unchanging value remains constant, illustrated across the categories labeled on the other axis.

Bar graphs highlight differences in magnitude between the categories, making it easy to assess variations in the changing variable compared to the baseline established by the unchanging value. This format is particularly useful when you want to show how one measurement varies with respect to another fixed reference point, providing an instantaneous snapshot of the differences involved.

The other graphical representations are less suitable for this scenario. For instance, pie charts are used to show the proportions of a whole, which does not lend itself well to comparing a variable that changes against a static value. Line graphs are typically used to depict trends over time, providing a clearer narrative of changes, which may not be suitable if the other variable does not fluctuate. Histograms are designed for showing frequency distributions of continuous data rather than comparing distinct groups or categories. Thus, a bar graph serves as the most effective tool for this specific kind of comparison.