Question

A snack box service offers its first box for free, then charges $11.99 for each additional box. Let C

be the cost of buying r snack boxes.
(a) Draw a graph with C as the vertical axis and x as the horizontal axis. Plot points to show
the cost of up to 5 snack boxes.
(b) Write an equation for C in terms of .
(c) What is the slope of the line represented by your equation? What does it represent in this
context?

Answer 1

a: In your plot, you'll have the following points, where the first coordinate is the number of boxes you get, and the second coordinate is how much you pay for them:

(0,0) <- Limit case: if you buy nothing, you pay nothing

(1,0) <- The first box is free

(2,11.99) <- You only pay the 2nd box

(3,23.98) <- You only pay the 2nd and 3rd box, 11.99*2=23.98

(4,35.97) <- You only pay the 2nd, 3rd and 4th box, 11.99*3=35.97

(5,47.96) <- You only pay the 2nd, 3rd, 4th and 5th box, 11.99*4=47.96

b: You pay $11.99 for each box you buy, except the first one. So, the rule is

`C=11.99(r-1)`

c: If you rewrite the equation in slope-intercept form, you have

`C=11.99r-11.99`

So, the slope is 11.99, which means that every time you increase the number of boxes by 1, the price will increase by 11.99, which is the same as saying that each box costs 11.99.