To make a graph, you typically need two sets of data: the independent variable and the dependent variable. The independent variable is the variable that you can control or manipulate in an experiment or study. It is usually plotted on the x-axis of a graph. The dependent variable, on the other hand, is the variable that is affected or influenced by the independent variable. It is usually plotted on the y-axis of a graph.

For example, let’s say you want to study the relationship between the amount of fertilizer used and the height of plants. In this case, the amount of fertilizer would be the independent variable, as you can control and change the amount used. The height of the plants would be the dependent variable, as it depends on the amount of fertilizer applied.

Once you have identified the independent and dependent variables, you can create a graph to visualize their relationship. You would plot the values of the independent variable on the x-axis and the corresponding values of the dependent variable on the y-axis. Each data point would represent a specific combination of the independent and dependent variables.

Graphs and functions are closely related. In fact, a graph can often represent a mathematical function. A function is a relationship between two variables, where each input (independent variable) corresponds to exactly one output (dependent variable). When you plot a function on a graph, you can see how the dependent variable changes as the independent variable varies.

For example, the equation y = 2x represents a linear function, where y is the dependent variable and x is the independent variable. By plugging in different values of x, you can calculate the corresponding values of y and plot them on a graph. The resulting graph would be a straight line with a slope of 2.

In summary, graphs are visual representations of the relationship between independent and dependent variables. They help us understand how changes in the independent variable affect the dependent variable. Functions, on the other hand, are mathematical representations of these relationships, and their graphs can provide insights into the behavior of the variables.