Final answer:
The independent variable is the amount of water used (w), while the dependent variable is the cost of the household's water bill (b), demonstrating that the bill cost is influenced by the water usage.
Step-by-step explanation:
In the situation where the relationship between the amount of water (w) a household uses and the cost of the household's water bill (b) is being studied, the independent variable is the amount of water the household uses. This is because it is the variable that is presumed to cause a change in the other variable. The dependent variable is the cost of the water bill, as it is expected to change in response to the amount of water used.
In terms of a linear equation, if we were to graph this relationship, we would place the amount of water used on the x-axis and the cost of the water bill on the y-axis, showing that the bill cost depends on the water usage amount. This is an example of a typical real-world context where linear equations are applied to understand how one variable affects another.