Question

A medium sized red velvet cake at the local bakery costs $20. The table below shows the total cost for each number of cakes.
Start by recording the cost of 1 cake.
Number of cakes Total cost in dollars
1
2
3
4
5
You got it!
Now, fill in the table to show the total cost of 2, 3, 4 and 5 cakes.
Number of cakes Total cost in dollars
1 20
2
3
4
5
Great job!
Use the table to plot the points on a coordinate plane.
Number of cakes Total cost in dollars
1 20
2 40
3 60
4 80
5 100
Good work!
The points are now connected with a line, m. Find the slope of line m.
x
y
m
0
1
2
3
4
5
6
7
8
9
10
11
12
0
10
20
30
40
50
60
70
80
90
100
110
120
Number of cakes
Total cost in dollars
Slope =

Answer 1

To find the slope of the line \( m \) that represents the relationship between the number of cakes and the total cost, we can use the formula for slope:

\[
\text{slope} (m) = \frac{\Delta y}{\Delta x}
\]

where \( \Delta y \) is the change in the total cost (y-values) and \( \Delta x \) is the change in the number of cakes (x-values).

From your data, we can calculate the slope using two points from the table. Let's take the points for 1 cake and 2 cakes:

- Point 1: (1, 20)
- Point 2: (2, 40)

Now, calculate the slope:

1. Change in total cost (\( \Delta y \)):
\[
\Delta y = 40 - 20 = 20
\]

2. Change in number of cakes (\( \Delta x \)):
\[
\Delta x = 2 - 1 = 1
\]

Now, plug these values into the slope formula:

\[
\text{slope} (m) = \frac{20}{1} = 20
\]

Thus, the slope of line \( m \) is:

\[
\text{slope} = 20
\]

This means that for every additional cake you buy, the total cost increases by $20.