Question

Zoe 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.

Answer 1

To fill in the table for the length of the scarf after 4 and 6 days:

1. Starting length: 6 cm
2. Daily increment: 1.5 cm per day

For 4 days:
- Length after 4 days = Starting length + (Daily increment × Number of days)
- Length after 4 days = 6 cm + (1.5 cm × 4) = 6 cm + 6 cm = 12 cm

For 6 days:
- Length after 6 days = Starting length + (Daily increment × Number of days)
- Length after 6 days = 6 cm + (1.5 cm × 6) = 6 cm + 9 cm = 15 cm

So the filled table is:
```
Number of days | Length of the scarf (cm)
----------------|---------------------------
4 | 12
6 | 15
```

Next, let's identify the slope of line \( m \), which represents the change in length of the scarf per day. Since Zoe knits 1.5 cm each day, this means the slope (the rate of change) of line \( m \) is:

- **Slope (m)** = Increase in length / Increase in days
- **Slope (m)** = 1.5 cm / 1 day = 1.5 cm/day

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