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To solve this problem, we need to find the correct function \( T(h) \) that represents the technician's tariff as a function of hours worked \( h \).

### Step-by-Step Solution:

1. **Interpret the graph**:
   - The horizontal axis (x-axis) represents the number of hours \( h \).
   - The vertical axis (y-axis) represents the tariff \( T(h) \), i.e., the amount to be paid.
   
   Looking at the graph, we observe the following points:
   - When \( h = 0 \), \( T(h) = 25 \), indicating that the base charge is 25 units.
   - The line appears to have a positive slope, which means the tariff increases as hours worked increase.
   
2. **Determine the slope**:
   - From the graph, the tariff at \( h = 1 \) is approximately 45 units.
   - To calculate the slope \( m \), use the formula for the slope of a line:
     \[
     m = \frac{T(1) - T(0)}{1 - 0} = \frac{45 - 25}{1 - 0} = 20
     \]
     So the slope is approximately 20 units per hour.

3. **Write the linear equation**:
   The general form of a linear equation is:
   \[
   T(h) = mh + b
   \]
   Where \( m \) is the slope and \( b \) is the y-intercept (base charge). From the graph, \( b = 25 \), and the slope is \( m = 20.83 \).

4. **Conclusion**:
   The correct equation that matches the data is:
   \[
   T(h) = 20.83h + 25
   \]
   This corresponds to option **a**.

Let me know if you want more details or have any questions!

### Related Questions:
1. How do you determine the slope of a line from a graph?
2. What is the meaning of the y-intercept in a real-life context?
3. How do you interpret the slope in terms of cost per hour?
4. How would the equation change if the base cost were different?
5. How can you verify a linear equation by plotting points?

#### Tip:
Always check the units on both axes of a graph to ensure the interpretation of slope and intercept is consistent with the given context.

Un técnico en reparaciones cobra una tarifa al cliente que depende de las horas de trabajo y del cobro base. El eje vertical corresponde a la tarifa a pagar T(h) y el eje horizontal corresponde a las horas trabajadas h. ¿Cuál es la función que describe la tarifa a pagar T(h)?

Learn how to determine the correct function T(h) that represents a technician's tariff based on hours worked. This problem covers key linear algebra concepts, including slope, y-intercept, and how to interpret them from a graph. Suitable for students in Grades 9-11.

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