Question

Jacob is a salesperson who sells computers at an electronics store. He 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 his sales that day. The equation p = 0.025x + 95 represents Jacob's total pay on a day on which he sells x dollars worth of computers. What is the y-intercept of the equation and what is its interpretation in the context of the problem?

Answer 1

The y-intercept of the equation ( p = 0.025x + 95 ) is 95. In the context of the problem, this means that even if Jacob doesn't make any sales ( x = 0 ), he still earns a base pay of $95 for that day.

Step-by-step explanation:

In the given equation ( p = 0.025x + 95 ), ( p ) represents Jacob's total pay, and ( x ) represents the total dollar amount of computers he sells. The y-intercept occurs when ( x = 0 ), which gives us the initial value of \( p ). In this case, when ( x = 0 ), the equation simplifies to p = 0.025(0) + 95 ), resulting in ( p = 95 ).

This means that even if Jacob doesn't make any sales, he still earns a base pay of $95 for that day. The y-intercept is a crucial point in understanding the starting point of Jacob's earnings before factoring in any sales commission. It represents a fixed income that Jacob receives regardless of his sales performance, highlighting the significance of the base pay component in his overall compensation structure.

In practical terms, the y-intercept signifies a guaranteed income for Jacob, providing a financial safety net irrespective of his daily sales. This information is valuable for both Jacob and the company, as it outlines a baseline cost for employing Jacob's services on any given day, regardless of his sales performance.