In conducting an experiment to obtain the graphs, a few variables must kept constant. What are these variables and explain why.
Without knowing what experiment you are talking about it is not possible to tell you exactly what variables must be kept constant. However, it is possible to discuss why some variables must be kept constant in any experiment.
When conducting an experiment, it is absolutely necessary to keep all the variables constant EXCEPT the one whose impact you are trying to measure.
Let's say you conduct an experiment and observe some change in the outcome. If you do not keep the other variables constant, you will not know if "your" variable is the one that caused the change you observe in the instrument.
You are generalising your question too much. However to obtain a graph of two variables we give a value to one variable and obtain the value of the other variable.
Example: T = 2Pi*sqrt(l/g). To obtain a relation of this type, we may have to conduct experiment, with different value of l. When you are doing the experiments for a particular l, the variable l is kept constant.To know the effect of only l, we keep g constant.
Graph is a relation or a function like, T = f(l,g) which implies.To test whether this hypothetical relation , through experiments, first you have create a controlled situation, where you hold g constant and l vary and record T. Then you hold l constant and conduct the rsperiment varying g. Based on the experiment you find whether the particular hypothesis holds good or ptherwise.
In the the above graph T = f(l, g) , we say l and g direct varibles and T is said to be indirect variable. In mathematics, l and g are said to be domains of T and T is said to be range .