Question

Samara is knitting a scarf. She has already knitted 6 centimeters and will knit 1.5 centimeters each day.
Fill in the table with the total length of the scarf after 4 and 6 days.
Number of days Length of the scarf (cm)
4
6
Nice!
Now that you've completed the table, plot the points on the coordinate plane.
Number of days Length of the scarf (cm)
4 12
6 15
Good work!
The points are now connected with a line, m. Find the slope of line m, or the change in the length of the scarf after one day.
x
y
m
0
1
2
3
4
5
6
7
8
9
10
0
1.5
3
4.5
6
7.5
9
10.5
12
13.5
15
Number of days
Length of the scarf (cm)
Slope =

Answer 1

To find the slope of line \( m \), we first need to understand what the slope represents in this context. The slope is the change in \( y \) (length of the scarf in centimeters) over the change in \( x \) (number of days).

From the information provided, we can see that:
- Samara starts with a length of 6 cm.
- She adds 1.5 cm each day.

Using this information, we can calculate the total length of the scarf after 4 and 6 days.

1. **After 4 Days**:
\[
\text{Length after 4 days} = 6 + (1.5 \times 4) = 6 + 6 = 12 \text{ cm}
\]

2. **After 6 Days**:
\[
\text{Length after 6 days} = 6 + (1.5 \times 6) = 6 + 9 = 15 \text{ cm}
\]

Thus, we can fill in the table as follows:

| Number of days | Length of the scarf (cm) |
|----------------|--------------------------|
| 4 | 12 |
| 6 | 15 |

Now to find the slope \( m \):

Given the points (4, 12) and (6, 15):

- Change in \( y \) (length) = \( 15 - 12 = 3 \)
- Change in \( x \) (days) = \( 6 - 4 = 2 \)

The slope \( m \) is calculated as:
\[
m = \frac{\text{Change in } y}{\text{Change in } x} = \frac{3}{2} = 1.5
\]

So, the slope of line \( m \) is 1.5.

### Final Answer
Slope = \( 1.5 \)