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The graph provided shows the function \( f(x) \), representing the total amount paid to a plumber, in dollars, for \( x \) hours of labor. The graph is a straight line, which indicates a linear relationship between the time worked and the amount paid.

To analyze the statements:

- A linear function means that the rate of change between the variables (in this case, hours and dollars) is constant.
- By examining the graph, the line increases by equal amounts for every additional hour of labor, suggesting a constant rate of change.

### Correct statement:
- **The function is linear because the values change by a constant rate per unit interval.**

This matches the first option: 
> "The function is linear because the values change by a constant rate per unit interval."

Would you like further details or clarifications?

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Here are 5 related questions for further exploration:

1. What is the slope of the line representing the plumber's rate per hour?
2. How would the graph change if the plumber charged a higher hourly rate?
3. If the plumber charged a flat fee plus an hourly rate, how would that affect the graph?
4. What does the y-intercept of the graph represent in this context?
5. Can a nonlinear graph ever represent a situation like this? Why or why not?

**Tip:** In a linear function, the slope represents the constant rate of change between the two variables. For real-world applications, this is often seen as a "rate" (e.g., dollars per hour).

Consider the graph of the function, f(x), which represents the total amount paid to a plumber, in dollars, for x hours of labor. Which statement is true?

This problem involves analyzing a graph that shows the total payment to a plumber based on hours worked. It tests the ability to identify a linear function by recognizing a constant rate of change, suitable for students in Grades 7-9.

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