https://file.aiquickdraw.com/mathbot/file/172609464516384t7kp3p.jpg

Let's break down the problem from the image step by step.

### Given:
The function is $ M(h) = 13h + 200 $.

### Part a: Write a word problem that could be represented by the function.
A possible word problem could be:

"A mechanic charges a base fee of $200 plus $13 for every hour of labor. Write a function that represents the total cost $ M(h) $ for $ h $ hours of labor."

### Part b: What does the 200 and the 13 represent in your problem?
- The **200** represents the **base fee** (or starting amount) that the mechanic charges regardless of the hours worked.
- The **13** represents the **hourly rate**, which is the cost for each hour of labor.

### Part c: Evaluate the function for $ h = 7 $ and write a sentence answer that fits with your problem.
To evaluate the function when $ h = 7 $:

\[
M(7) = 13(7) + 200 = 91 + 200 = 291
\]

A sentence could be: "For 7 hours of labor, the total cost charged by the mechanic would be $291."

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Would you like more details or clarifications on any part of this? 

Here are five additional questions to consider:
1. How would the word problem change if the base fee was reduced to $150?
2. What if the hourly rate doubled—how would the function change?
3. Could you create a different word problem that uses the same function, but with a different context?
4. What would the total cost be if the hours worked were increased to 10?
5. How would you interpret the function graphically, in terms of the slope and y-intercept?

**Tip:** Always double-check the units in a word problem to ensure consistency in your final answer.

Given the function M(h) = 13h + 200, write a word problem, explain what 200 and 13 represent, and evaluate the function for h = 7.

Solve a linear function word problem with M(h) = 13h + 200. Learn how to write a word problem based on this function, understand what the constants 200 and 13 represent, and evaluate the function for h = 7. Suitable for Grades 6-8.

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