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The problem involves determining the equation for the total cost $ C $ of manufacturing $ p $ phones based on the given graph. We need to find both the fixed cost and the cost per phone.

### Step-by-Step Solution:

1. **Identify the Slope of the Line:**
   - The slope $ m $ of the line can be calculated using the formula:
   \[
   m = \frac{\Delta C}{\Delta p}
   \]
   From the graph, when $ p = 0 $, $ C = 300 $ and when $ p = 10 $, $ C = 1200 $.

   So,
   \[
   m = \frac{1200 - 300}{10 - 0} = \frac{900}{10} = 90
   \]
   The slope $ m = 90 $ represents the cost per phone produced.

2. **Determine the Y-intercept:**
   - The y-intercept (fixed cost when no phones are produced) is visible on the graph as $ C = 300 $.

3. **Form the Equation:**
   - The equation of the line $ C $ is in the form:
   \[
   C = mp + b
   \]
   Substituting $ m = 90 $ and $ b = 300 $:
   \[
   C = 90p + 300
   \]

4. **Interpretation of the Slope:**
   - The slope $ m = 90 $ indicates that the cost to produce one additional phone is $90.

### Final Answer:
The equation for the total cost $ C $ of manufacturing $ p $ phones is:
\[
C = 90p + 300
\]

This means the fixed cost is $300, and the cost per phone is $90.

Would you like further details or have any questions?

---

1. How would the equation change if the fixed cost increased to $400?
2. What if the cost per phone decreased to $80?
3. How many phones can be produced for a total cost of $1500?
4. If 5 phones are produced, what is the total cost?
5. How does the cost change if no phones are produced?

**Tip:** Always check the units and context when interpreting slope and intercept values in word problems.

Austin is in the business of manufacturing phones. He must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. Let C represent the total cost, in dollars, of producing p phones in a given day. Write an equation for C then state the slope of the graph and determine its interpretation in the context of the problem.

Learn how to determine the total cost equation C = 90p + 300 for manufacturing phones based on the number of phones produced (p). This problem covers linear equations and the interpretation of slope and y-intercept in context. Suitable for students in Grades 9-10.

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