Question

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the above graph shows the payment scheme that company y offers to each of its salesmen. according to this payment scheme, part of a salesman’s monthly payment p in thousand dollars is based on the sales s in thousand dollars they make during the specific month.
choose the option that best answers the question.
what does the p-intercept represent in the graph?
the least amount in thousand dollars that a salesman will receive in a month.
the amount in thousand dollars that a salesman will receive in a month if they make sales between 1 thousand and 2 thousand dollars in this month
the minimum sales in thousand dollars required in a month before the payment scheme of company y takes effect in this month.
the increase in a salesman monthly payment for each 5 thousand additional sales they make in the month.

Explanation:

The P - intercept occurs when \( S = 0 \) (monthly sales is 0 thousand dollars). So it represents the amount a salesman gets when they have no sales (or the base amount), which is the least amount they will receive in a month (since sales can't be negative, this is the minimum payment). Let's analyze the options:

• Option 2: Talks about sales between 1k - 2k, but at P - intercept \( S = 0 \), so incorrect.
• Option 3: Mentions minimum sales for the scheme to take effect, but the scheme starts at \( S = 0 \) (since the line starts at \( S = 0 \)), so incorrect.
• Option 4: The slope represents the increase per additional sales, not the P - intercept, so incorrect.
• Option 1: Since at \( S = 0 \) (no sales), the P - intercept is the base payment, which is the least amount (as sales can't be negative, so this is the minimum they will receive in a month).

Answer:

The least amount in thousand dollars that a salesman will receive in a month.