Question

A scented candle company offers free shipping when you order scented candles from their website. Each scented candle costs $12. The graph below shows the relationship between the number of scented candles ordered and the total cost. What is the slope of this line?
Start by finding the change in vertical and horizontal distance from (2, 24) to (4, 48). In other words, what is the change in number of scented candles and the total cost from (2, 24) to (4, 48)?
x
y
m
(2, 24)(4, 48)
0
1
2
3
4
5
6
7
8
9
10
0
6
12
18
24
30
36
42
48
54
60
Number of candles
Total cost
Slope
=
vertical distance
horizontal distance
Great job!
Now, find the slope, or the change in vertical distance for a given change in horizontal distance. In other words, by how much does the total cost change every time you buy 1 scented candle?
2
24
x
y
m
(2, 24)(4, 48)
0
1
2
3
4
5
6
7
8
9
10
0
6
12
18
24
30
36
42
48
54
60
Number of candles
Total cost
Slope
=
vertical distance
horizontal distance
=
Nice!
What does the slope mean in this situation?
2
24
x
y
m
(2, 24)(4, 48)
0
1
2
3
4
5
6
7
8
9
10
0
6
12
18
24
30
36
42
48
54
60
Number of candles
Total cost
Slope
=
vertical distance
horizontal distance
=
12



Each additional scented candle costs $12.

The total cost of the order of scented candles is $12.

Answer 1

To find the slope of the line representing the relationship between the number of scented candles ordered and the total cost, we first need to determine the change in the vertical (total cost) and horizontal (number of candles) distances between the points (2, 24) and (4, 48).

1. **Identify the points:**
- Point A: (2, 24)
- Point B: (4, 48)

2. **Calculate the change in horizontal distance (change in number of candles):**
\[
\Delta x = 4 - 2 = 2
\]

3. **Calculate the change in vertical distance (change in total cost):**
\[
\Delta y = 48 - 24 = 24
\]

4. **Calculate the slope (m):**
- The slope is calculated using the formula:
\[
m = \frac{\Delta y}{\Delta x}
\]
Substituting in the changes we found:
\[
m = \frac{24}{2} = 12
\]

Now, let's interpret the slope:
The slope of 12 indicates that for every additional scented candle ordered, the total cost increases by $12. This makes sense knowing that each scented candle costs $12. Therefore, the relationship represented by the slope confirms that the total cost of an order of scented candles is directly proportional to the number of candles purchased, with each candle adding $12 to the total cost.