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To solve this problem, we need to determine the linear relationship between $ x $ (the dollar amount of computers sold) and $ P $ (Penelope's total pay).

Since the relationship between $ x $ and $ P $ is linear, we can express it as:
\[
P = mx + b
\]
where $ m $ is the slope (commission rate) and $ b $ is the y-intercept (base pay).

### Step 1: Find the Slope $ m $
The slope $ m $ is calculated using two points from the table. Let's use $(4000, 220)$ and $(5000, 260)$:

\[
m = \frac{P_2 - P_1}{x_2 - x_1} = \frac{260 - 220}{5000 - 4000} = \frac{40}{1000} = 0.04
\]

This means Penelope earns a commission of 4% of her sales.

### Step 2: Find the Y-Intercept $ b $
Now, substitute one of the points, such as $(4000, 220)$, and the slope $ m = 0.04 $ into the linear equation to solve for $ b $:

\[
220 = 0.04 \cdot 4000 + b
\]
\[
220 = 160 + b
\]
\[
b = 220 - 160 = 60
\]

This means Penelope’s base pay is $60.

### Step 3: Write the Linear Equation
Now we have the equation:
\[
P = 0.04x + 60
\]

### Step 4: Determine Penelope's Pay for $ x = 8000 $
Substitute $ x = 8000 $ into the equation:

\[
P = 0.04 \cdot 8000 + 60
\]
\[
P = 320 + 60 = 380
\]

### Conclusion
Penelope would be paid **$380** on a day when she sells $8000 worth of computers.

---

Would you like a deeper explanation on any step?

### Related Questions
1. What is the effect on Penelope's pay if her commission rate increases?
2. How would her pay change if her base pay increased by $20?
3. If Penelope sold $10,000 worth of computers, what would her pay be?
4. How would you determine her pay if the relationship was not linear?
5. What would happen to the slope if she only earned a 3% commission?

**Tip:** In a linear equation, the y-intercept represents a fixed amount or starting value, and the slope represents the rate of change.

Penelope is a salesperson who sells computers at an electronics store. She makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from her sales that day. Let P represent Penelope's total pay on a day on which she sells x dollars worth of computers. The table below has select values showing the linear relationship between x and P. Determine how much money Penelope would be paid on a day in which she sold $8000 worth of computers.

Learn how to calculate Penelope's total pay using a linear equation based on her base pay and commission rate. Given data includes values of x (computer sales amount) and P (total pay) for various sales levels. Solve for her pay when she sells $8000 worth of computers.

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