Ray is paid $15 for each hour he works. His total wages are w dollars, and his total hours worked are hours. One way to represent Ray's total wages is w=15h. Which of the following statements is true?
The dependent variable is the total wages earned.
In the equation w = 15h, total wages (w) depend on the number of hours worked (h), making total wages the dependent variable. As hours change, the total wages will also change, reflecting the relationship defined by the equation.
This statement accurately describes the relationship in the equation w = 15h. Here, total wages (w) are determined by the number of hours worked (h) multiplied by the hourly wage of $15. Since wages depend on the hours worked, they are the dependent variable in this scenario.
This statement is incorrect because the hourly rate is a constant value of $15 and does not change based on the hours worked. Rather, it serves as a multiplier for the independent variable (hours worked), making it an independent variable rather than a dependent one.
This is incorrect because total hours worked (h) is the independent variable in the equation. The total wages (w) depend on the hours worked, not the other way around. Thus, total hours worked cannot be classified as the dependent variable.
This statement is false because neither the hourly rate nor the total hours worked are both dependent variables. The hourly rate is a fixed value, while the total hours worked is independent, only affecting the dependent variable, total wages.
In the context of the equation w = 15h, the dependent variable is clearly the total wages earned, as they vary based on the hours worked. Understanding the distinction between dependent and independent variables is crucial in analyzing mathematical relationships, ensuring that the correct interpretations of changes in one variable due to variations in another are made.
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