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The question provided is as follows:

A factory worker's weekly earnings, \( y \), are given by the formula \( y = 25h + 110 \), where \( h \) represents the number of hours worked. Is the amount described by this equation discrete or continuous?

There are three answer options:
1. **Continuous**, because the earnings increase continuously as more hours are worked.
2. **Discrete**, because the worker can't work any hours, including fractions.
3. **Discrete**, because the number of hours worked must be a whole number.

### Answer Analysis:
This question tests the understanding of whether the relationship described by the equation \( y = 25h + 110 \) is discrete or continuous.

- **Continuous** means the function's values can take any number within a range, including fractions. In the context of time or hours worked, it assumes that the worker can work for any fraction of an hour (e.g., 1.5 hours).
  
- **Discrete** refers to scenarios where only specific values are possible (e.g., whole numbers only, such as working exactly 1 hour or 2 hours).

Here, the formula involves **hours worked**. Normally, hours can include fractions (e.g., 1.5 hours), which would make this a continuous scenario because time can be measured in increments smaller than a whole number. Therefore:

- The correct answer is **Continuous**, because the worker can potentially work any fractional number of hours, making the relationship continuous rather than restricted to whole numbers.

### Do you have any further questions or would you like more details?

Here are five follow-up questions to deepen understanding:
1. Can you explain why earnings based on hours worked could be considered continuous?
2. How would the situation change if hours worked could only be whole numbers?
3. What is the significance of the constant \(110\) in the formula \(y = 25h + 110\)?
4. How would you model earnings if overtime pay (extra for more than 40 hours) was included?
5. Could this equation be used for a different context, such as measuring a product's weight?

**Tip:** When determining if a variable is continuous or discrete, ask whether fractions or parts of the variable (like 1.5 hours) make sense in the real-world context.

A factory worker's weekly earnings are given by the equation y = 25h + 110, where h represents the number of hours worked. Is the amount described by this equation discrete or continuous?

Explore the concept of continuous and discrete data using the example of a factory worker's earnings, calculated using the equation y = 25h + 110. Learn about how hours worked can be measured and determine if the scenario represents a discrete or continuous relationship. Suitable for Grades 7-9.

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