Final answer:
The relationship between the profit or loss (y) and the number of calendars sold (x) is linear and described by the equation y = 7.92x - 983.60. The student council makes approximately $7.92 profit per calendar sold. If no calendars were sold, the loss would have been approximately $983.60.
Step-by-step explanation:
To determine the relationship between y, the profit or loss, and x, the number of calendars sold, we can create a linear equation based on the given data points: (80, -$350) and (200, $600). Just like the example of Svetlana's tutoring income, which is a linear function with a starting fee and a charge per hour, we can assume there is a fixed cost (the loss if they sold zero calendars) and a profit per calendar sold.
Let's denote the fixed cost as c and the profit per calendar as p. The general form of the equation would be y = px + c. To find the values of p and c, we use the two given data points to set up the following system of equations
- -350 = 80p + c
- 600 = 200p + c
Solving this system of equations, we subtract the first equation from the second to eliminate c and find the profit per calendar p. Once we have p, we can substitute back into either equation to find c, the fixed cost.
By doing the calculations, we get
950 = 120p
p = $7.92 (approximately)
Then substituting p into the first equation:
-350 = 80($7.92) + c
c = -$983.60 (approximately)
Therefore, the equation that describes the relation between profit or loss y and the number of calendars x sold is:
y = 7.92x - 983.60
The student council makes approximately $7.92 of profit by selling each calendar. If they had sold no calendars, they would have incurred a loss of approximately $983.60.