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Let's go through the questions one by one:

1. **Slope of $ P(n) = 460n - 12880 $:**
   - The slope is the coefficient of $ n $, which is 460.
   - This means the company earns $460 per computer sold.

2. **Vertical Intercept:**
   - The vertical intercept is found by setting $ n = 0 $.
   - $ P(0) = 460(0) - 12880 = -12880 $.
   - The ordered pair is $ (0, -12880) $.
   - This means that if no computers are sold, the company will lose $12,880.

3. **Horizontal Intercept:**
   - To find the horizontal intercept, set $ P(n) = 0 $ and solve for $ n $.
   - $ 460n - 12880 = 0 $.
   - $ 460n = 12880 $.
   - $ n = 28 $.
   - The ordered pair is $ (28, 0) $.
   - This means the company needs to sell 28 computers to break even, earning $0 profit.

4. **Evaluate $ P(35) $:**
   - $ P(35) = 460 \times 35 - 12880 $.
   - $ P(35) = 16100 - 12880 = 3220 $.
   - The ordered pair is $ (35, 3220) $.
   - This means if the company sells 35 computers, they will earn a profit of $3,220.

Would you like to go into any more detail on these steps or have any other questions?

### 5 Relative Questions:
1. What does a positive slope in a profit function indicate about a company's sales?
2. How would the company's profit change if the slope were negative?
3. What is the significance of the vertical intercept in a real-world scenario for a business?
4. How can we determine the breakeven point from a profit function graphically?
5. What would the profit be if the company sold 50 computers?

### Tip:
Always interpret the meaning of intercepts and slopes in the context of the problem to better understand real-world implications.

The function P(n) = 460n - 12880 represents a computer manufacturer's profit P(n) when n computers are sold.

Explore how to solve the profit function P(n) = 460n - 12880 to determine a company's earnings per computer, break-even points, and profit evaluation. This problem is suitable for high school students in Grades 9-12 and covers key linear function concepts.

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