Graphing data is one of the most common and useful ways of presenting data for further interpretation. The two variables are set as the axes and the points plotted. It is possible to get a qualitatively idea of any relationship between the variables by the shape of the line plotted.
Dependency in graphing means the relationship that the two variables have with one another.
There are only a few possible shapes of graph lines with which students should be familiar. It should be possible for a student to state the type of relationship between independent variable and the dependent variable simply by looking at the graph. This does pre-suppose that the graph has sufficient points plotted. Clearly two points can always be joined by a straight line!
The variable that is chosen and controlled is called the independent, or input variable. This should always be plotted along the x-axis. The dependent, or output variable is plotted along the y-axis.
If the chosen independent variable has no effect on the dependent variable and the other variables are perfectly controlled the line is flat and the gradient (slope) is zero.
Proportionality between variables may be direct or inverse. In a direct proportionality a straight line results when the dependent variable is plotted against the independent variable. The gradient shows the dependency, the proportionality constant. The intercept with the y-axis shows any constant that is added to the proportionality.
However, if the variables are inversely proportional a curve is produced when they are plotted against each other. This makes inverse proportionality difficult to see qualitatively. For example, the volume of an ideal gas is inversely proportional to the pressure. A plot of pressure against volume shows qualitately that there is an inverse relationship, but it is impossible to say whether it is a simple inverse relationship.
If inverse proportionality is suspected then a graph of the inverse of the dependent variable against the independent variable gives a straight line.
If the two variables are multiplied together and plotted against one or other of them, then a flat line should result. This can be seen in the plot of PV against P for an ideal gas when complared to a real gas.
Graph PV against P
When the relationship is complex, such as a squared, or logarithmic relationship, the graph line is a curve. Further data analysis is needed to come to reasonable conclusions. There are many areas of the syllabus where this kind of graph is seen, for example in rates of reaction. A plot of gas evolved over time during a reaction shows qualitatively that the rate of evolution slows down over time, but further analysis is required to obtain quantitative data.
If the relationship between variables is periodic the graph line shows a repeating pattern.
One example is the plot of 1st ionisation energy against atomic number. The shape of the graph between atomic numbers 3 and 10 appears to repeat between atomic numbers 11 and 18. This can be explained by an in-depth study of atomic orbitals.
If the points appear to be random then something is not right with the experiment. The dependent variable is being changed by some other factor that has not been taken into account, but has little or nothing to do with the independent variable.