Question

Venita is sewing new curtains. The table below shows the relationship between the number of stitches in a row and the length of the row.

Number of Stitches Length (cm)
7 1
21 3
28 4
42 6
What is the relationship between the number of stitches and the length?

Answer 1

To understand the relationship between the number of stitches and the length of the row, let's first organize the data:

- When there are 7 stitches, the length is 1 cm.
- When there are 21 stitches, the length is 3 cm.
- When there are 28 stitches, the length is 4 cm.
- When there are 42 stitches, the length is 6 cm.

Now, let's examine the data to identify a pattern.

1. **Calculate the stitches per cm:**
- For 1 cm: \( \frac{7 \text{ stitches}}{1 \text{ cm}} = 7 \text{ stitches/cm} \)
- For 3 cm: \( \frac{21 \text{ stitches}}{3 \text{ cm}} = 7 \text{ stitches/cm} \)
- For 4 cm: \( \frac{28 \text{ stitches}}{4 \text{ cm}} = 7 \text{ stitches/cm} \)
- For 6 cm: \( \frac{42 \text{ stitches}}{6 \text{ cm}} = 7 \text{ stitches/cm} \)

The number of stitches per cm is consistent at 7 stitches for each row length.

2. **Create an equation for the relationship:**
Given that the relationship between the number of stitches (S) and the length (L) can be expressed as:

\[
S = 7L
\]

This equation indicates that the number of stitches is directly proportional to the length of the row, with a constant of proportionality equal to 7.

**Conclusion:**
The relationship between the number of stitches and the length of the row is linear, represented by the equation \( S = 7L \), indicating that for every centimeter of length, there are 7 stitches.