Question

Members of the student concil 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 of 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 1

a)
`y=8x-1000`

b)
`profit=\$8`

c) They'd have lost $1000 if they had sold no calendars.

Explanation:

a) The equation of the line in Slope-Intercept form is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

In this case we know that "y" represents the profit of loss and "x" the number of calendars sold.

Then, according to the exercise, the line passes through these two points:

`(80,-360)` and
`(200,600)`

Then, we can find the slope of the line with the formula
`m=(y_2-y_1)/(x_2-x_1)`

`m=(-360-600)/(80-200)=8`

Now, we can substitute the slope and one of those points into
`y=mx+b` and solve for "b":

`600=8(200)+b\\\\b=-1000`

Then, subtituting values, we get that the equation that describes the relation between the profit of loss and the number of calendars sold, is:

`y=8x-1000`

b) The slope of the line is the profit they made from selling each calendar

`profit=8`

c) The y-intercept is the amount they would have lost if they had sold no calendars:

`b=-1000`

They'd have lost $1000 if they had sold no calendars.