2. 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?
Answer: A
The dependent variable is the total wages earned.
In the equation w = 15h, the total wages earned, represented by w, depend on the total hours worked, h. Therefore, the total wages earned is the dependent variable in this context.
A) The dependent variable is the total wages earned.
This statement is correct because in the equation w = 15h, the total wages (w) vary based on the number of hours worked (h), making it the dependent variable. As h changes, w changes accordingly, which is the characteristic of a dependent variable.
B) The dependent variable is the hourly rate.
This statement is incorrect. The hourly rate of $15 is a constant multiplier in this context and does not depend on the variable hours worked. Instead, it is an independent variable that influences the total wages earned.
C) The dependent variable is the total hours worked.
This statement is incorrect. Total hours worked (h) is an independent variable that influences the total wages (w). The total hours worked do not change based on the wages; rather, it is the wages that depend on how many hours Ray has worked.
D) The dependent variables are both the hourly rate and the total hours worked.
This statement is incorrect. In the equation w = 15h, only the total wages (w) is the dependent variable. The hourly rate and total hours worked are independent variables that interact to determine the total wages.
Conclusion
The correct answer is A, as the total wages earned directly depend on the total hours worked, making it the dependent variable. Options B, C, and D misinterpret the roles of the variables in the equation and do not accurately reflect the relationship defined in the context. Thus, A is the only statement that correctly identifies the dependent variable.