Questions to Ask when Interpreting a Graph

A graph of A vs. B has quantity A on the vertical axis, quantity B on the horizontal axis.

Any graph you sketch should be labeled in the following manner:

• The title of the graph will contain the identification A vs. B, with A and B being the appropriate names of the things being graphed.
• Each axis should be labeled and the units should be included in the label (e.g., for a graph of velocity v vs. clock time t, the vertical axis might be labeled 'v (cm/s)' and the horizontal axis 't (sec)').

When you analyze a graph you typically ask the following questions:

• What quantity is graphed on the vertical axis and what does this quantity tell you about the situation being graphed?
• What quantity is graphed on the horizontal axis and what does this quantity tell you about the situation being graphed?
• What does the highest point of the graph represent in terms of the situation?
• What does the lowest point of the graph represent in terms of the situation?
• What does the rise between two points of the graph mean in terms of the situation?
• What does the run between two points of the graph mean in terms of the situation?
• What does the slope of the graph represent in terms of the situation?
• Where is the slope greatest, where is the slope least, and what does this tell you about the situation
• Where is the slope zero, and what does this tell you about the situation?

• What does the midpoint height of a line segment on the graph represent and what does this tell you about the situation?
• What does the width of the trapezoid beneath the line segment represent and what does this tell you about the situation?
• What does the area of the trapezoid beneath the line segment represent and does this quantity tell you anything important about the situation, and if so what?