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 =
Excellent!
What does the slope mean in this situation?
2
3
x
y
m
(4, 12)(6, 15)
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
=
vertical distance
horizontal distance
=
1.5
After each
, the length of the scarf increases by 1.5 more
.
day
centimeter
days
centimeters
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 =
Excellent!
What does the slope mean in this situation?
2
3
x
y
m
(4, 12)(6, 15)
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
=
vertical distance
horizontal distance
=
1.5
After each
, the length of the scarf increases by 1.5 more
.
day
centimeter
days
centimeters
Answers
GPT-4o mini
Let's summarize the task step by step:
1. **Total Length of the Scarf After 4 and 6 Days**:
- **Total Length after 4 Days**:
- Initial length: 6 cm
- Daily increase: 1.5 cm/day
- After 4 days:
\[
6 + (1.5 \times 4) = 6 + 6 = 12 \text{ cm}
\]
- **Total Length after 6 Days**:
- After 6 days:
\[
6 + (1.5 \times 6) = 6 + 9 = 15 \text{ cm}
\]
2. **Fill in the Table**:
- Number of days | Length of the scarf (cm)
- 4 | 12
- 6 | 15
3. **Plot the Points on the Coordinate Plane**:
- Points:
- (4, 12)
- (6, 15)
4. **Finding the Slope of Line m**:
- The formula for slope \( m \) is given by:
\[
m = \frac{\text{change in } y}{\text{change in } x}
\]
- From points (4, 12) to (6, 15):
- Change in \( y \): \( 15 - 12 = 3 \)
- Change in \( x \): \( 6 - 4 = 2 \)
- Thus the slope \( m \) is:
\[
m = \frac{3}{2} = 1.5
\]
5. **Interpreting the Slope**:
- The slope \( 1.5 \) in this context means:
- **After each day, the length of the scarf increases by 1.5 centimeters**.
So, the final summary of your statements can be organized as follows:
- **Slope** = 1.5
- After each **day**, the length of the scarf increases by **1.5 centimeters.**
1. **Total Length of the Scarf After 4 and 6 Days**:
- **Total Length after 4 Days**:
- Initial length: 6 cm
- Daily increase: 1.5 cm/day
- After 4 days:
\[
6 + (1.5 \times 4) = 6 + 6 = 12 \text{ cm}
\]
- **Total Length after 6 Days**:
- After 6 days:
\[
6 + (1.5 \times 6) = 6 + 9 = 15 \text{ cm}
\]
2. **Fill in the Table**:
- Number of days | Length of the scarf (cm)
- 4 | 12
- 6 | 15
3. **Plot the Points on the Coordinate Plane**:
- Points:
- (4, 12)
- (6, 15)
4. **Finding the Slope of Line m**:
- The formula for slope \( m \) is given by:
\[
m = \frac{\text{change in } y}{\text{change in } x}
\]
- From points (4, 12) to (6, 15):
- Change in \( y \): \( 15 - 12 = 3 \)
- Change in \( x \): \( 6 - 4 = 2 \)
- Thus the slope \( m \) is:
\[
m = \frac{3}{2} = 1.5
\]
5. **Interpreting the Slope**:
- The slope \( 1.5 \) in this context means:
- **After each day, the length of the scarf increases by 1.5 centimeters**.
So, the final summary of your statements can be organized as follows:
- **Slope** = 1.5
- After each **day**, the length of the scarf increases by **1.5 centimeters.**