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To determine Paisley's base pay, we need to analyze the linear relationship between $ x $ (the amount of computer sales) and $ P $ (Paisley's total pay). We assume the relationship between $ x $ and $ P $ follows the equation of a line:

\[
P = mx + b
\]

where:
- $ m $ is the commission rate (slope),
- $ b $ is the base pay (y-intercept), which we are asked to find.

### Step 1: Find the Slope $ m $
Using two points from the table, we can calculate $ m $.

Let’s choose the points $ (1000, 125) $ and $ (2000, 160) $.

The slope formula is:
\[
m = \frac{P_2 - P_1}{x_2 - x_1}
\]

Substitute the values:
\[
m = \frac{160 - 125}{2000 - 1000} = \frac{35}{1000} = 0.035
\]

Thus, the commission rate $ m $ is 0.035.

### Step 2: Set Up the Equation with Known Values
Now, substitute $ m = 0.035 $ into the linear equation:
\[
P = 0.035x + b
\]

### Step 3: Solve for $ b $ (Base Pay)
Using one of the points to solve for $ b $, let's use $ (1000, 125) $:

\[
125 = 0.035 \cdot 1000 + b
\]

Calculate $ 0.035 \cdot 1000 $:
\[
125 = 35 + b
\]

Now, isolate $ b $:
\[
b = 125 - 35 = 90
\]

### Conclusion
The base pay, regardless of computer sales, is:
\[
\boxed{90}
\]

---

Would you like more details or have any questions?

### Related Questions
1. What is the commission rate Paisley receives on her sales?
2. How would the equation change if her base pay increased?
3. Can you find her pay if she sells $5000 worth of computers?
4. What would her total pay be if she made no sales in a day?
5. How would the solution change if the relationship were not linear?

### Tip
When analyzing linear relationships, the y-intercept represents the value that doesn’t depend on the variable—in this case, Paisley's base pay.

Paisley 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 Paisley'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 the base pay Paisley makes regardless of computer sales.

Learn how to calculate Paisley's base pay using a linear equation with given sales values. This problem involves finding the slope (commission rate) and the y-intercept (base pay) from a set of data points. Suitable for students in Grades 8-10.

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