Carla earns $9 per hour working at a clothing store. She is writing a function to show the relationship between her hours worked h, and her wages earned w. In Carla’s function, what does the independent variable represent? step by step

To solve this problem step by step, let's break it down:

### Step 1: Understand the Function
Carla is creating a function that shows the relationship between the hours she works (denoted by $ h $) and the wages she earns (denoted by $ w $). The function can be written as:
\[
w(h) = 9h
\]
This function states that the wages $ w $ are calculated by multiplying the number of hours worked $ h $ by her hourly rate of $9.

### Step 2: Identify the Independent and Dependent Variables
- **Independent Variable**: The independent variable is the variable that you can change or control. In this case, it's the number of hours Carla works, $ h $.
- **Dependent Variable**: The dependent variable is the variable that depends on the value of the independent variable. Here, it's the wages Carla earns, $ w $.

### Step 3: Determine What the Independent Variable Represents
The independent variable $ h $ represents the number of hours Carla works. This means that the amount of time she works is what she can control or choose, and her earnings will depend on this value.

### Conclusion:
In Carla’s function, the independent variable $ h $ represents the **number of hours she works**.

Would you like more details on how this relates to functions in general or any other aspect? Here are some related questions:

1. What is a dependent variable in this context, and how does it relate to the independent variable?
2. How would the function change if Carla got a raise to $12 per hour?
3. Can you graph the function to visually represent the relationship between hours worked and wages earned?
4. How would you describe the slope of the function in this context?
5. If Carla worked 15 hours, how much would she earn according to the function?

**Tip:** In any function, the independent variable is the input, the value you can control, while the dependent variable is the output, which changes in response to the input.

Explore Carla's function that relates hours worked to wages earned at $9 per hour. Understand the concept of independent and dependent variables in functions. Suitable for students in Grades 6-8.

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