12.4 - Reading Graphs & Drawing Conclusions

Reading a value off the graph

• To read off a value (e.g. the volume of gas at 30 seconds): go up from 30 s on the x-axis to the curve, then across to the y-axis and read off the value.
• Always draw both dashed construction lines on the graph to show where your number came from.

Interpolation vs extrapolation

• Interpolation - Reading a value between your plotted points.
• Extrapolation - Estimating a value beyond your plotted points by extending the line. Avoid this unless asked, because you can't be sure the curve continues the same way.

Describing a trend

A complete trend answer needs three things: the direction of the graph, figures from the axes to back it up, and any change (such as where the curve levels off).

As [independent variable] increases, [dependent variable] increases (or decreases), from [figure] to [figure], then levels off at [value].

Example: "As time increases, the volume of gas increases quickly at first, from 0 to about 40 cm³ in the first 20 seconds, then more slowly, before levelling off at 60 cm³ once the reaction has finished."

Directly proportional relationships

• A relationship is only directly proportional when its graph is a straight line through the origin (doubling one variable doubles the other).
• A curve, or a straight line that does not pass through the origin, is not directly proportional, even if it rises steadily.

Drawing a conclusion

• A conclusion states how the independent variable affects the dependent variable.
• It always names both variables and states how they change together:

As the [independent variable] increased, the [dependent variable] increased (or decreased).

• Example: "As the concentration of the acid doubled, the mean rate roughly doubled."
• Where the data supports it, include numbers to describe the relationship rather than just giving a direction.

Match the conclusion to the data

• A conclusion must only describe what the data actually shows.
• Don't extend the conclusion beyond the range of values tested, and only claim a mathematical relationship (like doubling) if all your results support it.

What a conclusion is not

• Not a single reading - Stating one value (e.g. "the rate was 2.5 cm³/s") doesn't link the two variables.
• Not an explanation - A conclusion states what happened (the rate increased as concentration increased), not why (which requires collision theory).