A company pays $10 per hour for up to 8 hours of work, and $15 per hour for overtime hours (hours beyond 8). For overtime hours, what is the slope of the line for total pay?

For overtime hours (beyond 8 hours), the company pays $15 per hour. The slope of the line for total pay is the rate at which the total pay increases with each additional hour of overtime. 

Since the company pays $15 per overtime hour, the slope of the line for total pay in the overtime range is:

\[
\text{slope} = 15 \, \text{(dollars per hour)}
\]

Thus, the slope is **15**.

Would you like a more detailed breakdown or have any questions?

Here are 5 related questions to expand on this topic:
1. What would the total pay be for working 10 hours?
2. How would the pay formula look if the company had different rates for overtime tiers (e.g., 1.5 times the normal rate)?
3. If the hourly rate for normal hours increases to $12, how would that change the total pay for 10 hours?
4. How would the slope change if the overtime pay was $20 instead of $15?
5. How many hours would you need to work to earn $200 in total?

**Tip:** The slope of a line in such problems represents the rate of change of one quantity with respect to another, in this case, the rate of change of total pay with respect to hours worked.

Learn how to calculate the slope of the total pay for overtime hours in a piecewise function where regular pay is $10 per hour and overtime pay is $15 per hour. Understand how the slope represents the rate of change in total pay with respect to overtime hours. Suitable for students in Grades 8-10.

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