Question

ella 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 ellas 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 ella makes regardless of computer sales. x | p 4500 | 145 8500 | 225 9500 | 245

Explanation:

Step1: Find the slope (commission rate)

The slope \( m \) of a line through two points \( (x_1, P_1) \) and \( (x_2, P_2) \) is given by \( m=\frac{P_2 - P_1}{x_2 - x_1} \). Using the points \( (4500, 145) \) and \( (8500, 225) \):
\( m=\frac{225 - 145}{8500 - 4500}=\frac{80}{4000}=0.02 \)

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( P - P_1=m(x - x_1) \). Using the point \( (4500, 145) \) and \( m = 0.02 \):
\( P-145 = 0.02(x - 4500) \)

Step3: Simplify the equation

Expand the right - hand side: \( P-145=0.02x-90 \)
Add 145 to both sides: \( P = 0.02x+55 \)
The base pay is the value of \( P \) when \( x = 0 \) (since \( x = 0 \) means no sales). In the equation \( P=0.02x + 55 \), when \( x = 0 \), \( P = 55 \). We can also verify with another point. Let's use \( (9500,245) \). Substitute \( x = 9500 \) into \( P=0.02x + 55 \): \( P=0.02\times9500+55=190 + 55=245 \), which matches the given table.

Answer:

The base pay Ella makes regardless of computer sales is 55 dollars.