Line Graphs - How Quickly Things Change

In Plotting Lines..., we introduced the idea of line graphs and in A Matter of Scale: Using Line Charts for Quantity Conversion suggested how they might be used to provide a graphical tool for converting values across different measurement scales.

The other main way of using line graphs is to show how one or more quantities change over time. The OpenLearn unit Exploring distance time graphs looks in some detail at one particular class of time based line graph, that is, the distance time graph, which plots the distance travelled by an object from a starting point against the time spent travelling from that point.

If you read through all of section 7 from that unit (starting with 7.1 Modeling a Journey: Introduction and finishing with 7.12: Distance-time graphs: summing up), you will see how the "steepness" of the graph at any point - that is, it's gradient - describes the speed at that time (that is, if the measure the slope of a distance-time graph, it tells us the speed the object was travelling at, at that time).

This sort of makes sense in a visual way too: the steepness of the slope (gradient) of the graph at any point shows how quickly things were changing at that point.

If you take a bird's eye view of a point riding along the graph, you can really get a feel for what the gradient is telling you about how thing might go in the future...

For example, here is visualisation showing how house prices changed in the UK from 1953 to 2006, where the average house price for each year is depicted as the height above ground of a rollercoaseter track - and you're riding on it...

To my mind, the movie expresses very well the different rates of change in house price inflation (and depreciation) over that time... and what's more, now you have that "visualisation" in mind, you don't necessarily need to generate and watch rollercoaster movies for other line graphs in order to invoke the visualisation - you can do it in mind's eye just by looking at the gradient of the graph...