Identify the independent variable in the following situation: A garden hose runs for ℎ hours and produces 𝑔 gallons of water.
We can think of this situation in terms of input and output. Something goes in, there’s a rule that changes that amount, and then we get an output. What we put in, our input, represents the independent variable. The output is the dependent variable. It depends on both, the input and the rule.
In this case, we take the number of hours and we put it in. Some rule happens. And the output is the number of gallons of water that is produced. ℎ hours go in and 𝑔 gallons of water come out. This makes ℎ, the number of hours, the independent variable.