Brian spent a certain amount of money to set up a lemonade stand. The graph below shows the amount he earns, y, by selling x glasses of lemonade.

Question

Which of the following situations is represented by the graph below?

A. 
Brian spent $80 initially to set up the stand, and for every glass of lemonade he sold, he earned $1.05.

B. 
Brian spent $80 initially to set up the stand, and for every glass of lemonade he sold, he earned $0.20.

C. 
Brian earned $80 initially, and for every glass of lemonade he sold, he earned $1.25.

D. 
Brian earned $40 initially, and for every glass of lemonade he sold, he earned $0.25.

GPT-4o mini · Answer

To determine the situation represented by the graph of Brian's lemonade stand earnings, we need to consider two factors: the initial amount spent (or earned), and the earnings per glass sold.

The graph's y-intercept represents the initial amount (fixed costs) and the slope represents the earnings per glass sold.
If Brian spent money to set up the stand, this would show as a negative value on the graph because it reduces the total earnings.
If Brian earned money initially, that would reflect as a positive y-intercept.

Given the options:

A. Brian spent $80 initially to set up the stand, and for every glass of lemonade he sold, he earned $1.05.

This would start at -80 and increase at a slope of 1.05, which would be a downward initial value.

B. Brian spent $80 initially to set up the stand, and for every glass of lemonade he sold, he earned $0.20.

This would also start at -80 (downward initial value) and increase at a slope of 0.20.

C. Brian earned $80 initially, and for every glass of lemonade he sold, he earned $1.25.

This would start at 80 and increase at a slope of 1.25, which reflects initial earnings.

D. Brian earned $40 initially, and for every glass of lemonade he sold, he earned $0.25.

This would start at 40 and increase at a slope of 0.25, reflecting an initial positive value.

From this analysis:

Options A and B represent a situation where he spent money to set up the stand (negative initial y-values).
Options C and D represent earnings, with a positive initial y-value.

Based on the context of typical lemonade stands, it’s more common to lose money initially until reaching profitability, but we cannot definitively choose the correct answer without the graph to analyze the intercept and slope.

If provided with the intercept and the slope from the graph, we could match one of the options more accurately. Please check the graph for starting point (y-intercept) and slope (increase per glass) to determine which of these scenarios fits best.

If the y-intercept is a positive number and indicates earnings, then C or D may be the answer. If it is negative and represents upfront costs, the answer would be A or B. My recommendation is based on that analysis.