11. members of the student council are conducting a fundraiser by selling school calendars. after selling 80…

11. members of the student council are conducting a fundraiser by selling school calendars. after selling 80 calendars, they had a loss of $360. after selling 200 calendars, they had a profit of $600. write an equation that describes the relation between y, the profit or loss, and x, the number of calendars sold. how much profit did they make from selling each calendar? how much would they have lost if they had sold no calendars?

11. members of the student council are conducting a fundraiser by selling school calendars. after selling 80 calendars, they had a loss of $360. after selling 200 calendars, they had a profit of $600. write an equation that describes the relation between y, the profit or loss, and x, the number of calendars sold. how much profit did they make from selling each calendar? how much would they have lost if they had sold no calendars?

Answer

Explanation:

Step1: Find the slope (profit per calendar)

The two - point form for the profit function is based on the points $(x_1,y_1)=(80, - 360)$ and $(x_2,y_2)=(200,600)$. The slope $m$ (profit per calendar) is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. $m=\frac{600-(-360)}{200 - 80}=\frac{600 + 360}{120}=\frac{960}{120}=8$

Step2: Find the y - intercept (loss when no calendars are sold)

Use the point - slope form of a line $y - y_1=m(x - x_1)$ with the point $(x_1,y_1)=(80,-360)$ and $m = 8$. $y-(-360)=8(x - 80)$ $y + 360=8x-640$ $y=8x-640 - 360$ $y=8x - 1000$ When $x = 0$, $y=-1000$.

Step3: Write the equation

The equation that describes the relation between $y$ (profit or loss) and $x$ (number of calendars sold) is $y = 8x-1000$.

Answer:

The equation is $y = 8x-1000$. The profit from selling each calendar is $$8$. The loss if they had sold no calendars is $$1000$.