Which graphical representation displays distinct values of qualitative data on the x-axis and frequencies on the y-axis?

A bar chart is the appropriate graphical representation for illustrating distinct values of qualitative data on the x-axis, with frequencies indicated on the y-axis. In a bar chart, each category, or distinct value, is represented by a separate bar, with the height of each bar corresponding to the frequency or count of that category. This visual format allows for easy comparison across different categories, making it simple to see which values are more or less frequent.

In contrast, a pie chart represents percentages of a whole and does not display frequencies directly on an axis. A line graph is typically used for quantitative data, showing trends over time or continuous data, rather than distinct qualitative categories. Lastly, a histogram is designed to show the distribution of quantitative data across intervals or bins, not distinct qualitative values. Therefore, the bar chart effectively meets the criteria set out in the question.