Question
Check all of the statements that are TRUE about the scenario represented:
Months of growth
3
5
8
9
15
Length of hair (inches)
8
11
15.5
17
26
(3 points)
Responses
The y-intercept (0, 3.5) represents the amount of time it takes to grow 3 1/2 inches of hair.
The y-intercept (0, 3.5) represents the amount of time it takes to grow 3 1/2 inches of hair.
The equation of the line would be y = 3.5 x + 3/2
The equation of the line would be y = 3.5 x + 3/2
The slope 3/2 means that hair can grow 1.5 inches every month
The slope 3/2 means that hair can grow 1.5 inches every month
The y-intercept (0, 3.5) means that at the starting time, there was 3.5 inches of hair
The y-intercept (0, 3.5) means that at the starting time, there was 3.5 inches of hair
The slope 3/2 means that 2 inches of growth happens every 3 months.
The slope 3/2 means that 2 inches of growth happens every 3 months.
The equation of the line would be y = 3/2 x + 3 1/2
Months of growth
3
5
8
9
15
Length of hair (inches)
8
11
15.5
17
26
(3 points)
Responses
The y-intercept (0, 3.5) represents the amount of time it takes to grow 3 1/2 inches of hair.
The y-intercept (0, 3.5) represents the amount of time it takes to grow 3 1/2 inches of hair.
The equation of the line would be y = 3.5 x + 3/2
The equation of the line would be y = 3.5 x + 3/2
The slope 3/2 means that hair can grow 1.5 inches every month
The slope 3/2 means that hair can grow 1.5 inches every month
The y-intercept (0, 3.5) means that at the starting time, there was 3.5 inches of hair
The y-intercept (0, 3.5) means that at the starting time, there was 3.5 inches of hair
The slope 3/2 means that 2 inches of growth happens every 3 months.
The slope 3/2 means that 2 inches of growth happens every 3 months.
The equation of the line would be y = 3/2 x + 3 1/2
Answers
GPT-4o mini
To evaluate the truth of each statement, let's analyze the information provided and the potential meaning behind the data:
1. **The y-intercept (0, 3.5) represents the amount of time it takes to grow 3 1/2 inches of hair.**
- **False**: The y-intercept (0, 3.5) actually represents the length of hair at time zero, not the time it takes to grow that amount.
2. **The equation of the line would be y = 3.5 x + 3/2.**
- **False**: This equation does not represent a proper slope-intercept form based on the data.
3. **The slope 3/2 means that hair can grow 1.5 inches every month.**
- **True**: A slope of 3/2 means that for every month (1 month), the hair grows 1.5 inches.
4. **The y-intercept (0, 3.5) means that at the starting time, there was 3.5 inches of hair.**
- **False**: Based on your prior data points, it appears the growth starts at a different value. The y-intercept would need to be calculated based on the data provided.
5. **The slope 3/2 means that 2 inches of growth happens every 3 months.**
- **True**: A slope of 3/2 implies that for every 2 inches of growth, 3 months have passed (2 inches per 3 months).
6. **The equation of the line would be y = 3/2 x + 3 1/2.**
- **False**: While the slope is 3/2 (1.5), the y-intercept would be represented differently based on actual data points provided.
In summary, the statements that are TRUE based on the information given are:
- The slope 3/2 means that hair can grow 1.5 inches every month.
- The slope 3/2 means that 2 inches of growth happens every 3 months.
1. **The y-intercept (0, 3.5) represents the amount of time it takes to grow 3 1/2 inches of hair.**
- **False**: The y-intercept (0, 3.5) actually represents the length of hair at time zero, not the time it takes to grow that amount.
2. **The equation of the line would be y = 3.5 x + 3/2.**
- **False**: This equation does not represent a proper slope-intercept form based on the data.
3. **The slope 3/2 means that hair can grow 1.5 inches every month.**
- **True**: A slope of 3/2 means that for every month (1 month), the hair grows 1.5 inches.
4. **The y-intercept (0, 3.5) means that at the starting time, there was 3.5 inches of hair.**
- **False**: Based on your prior data points, it appears the growth starts at a different value. The y-intercept would need to be calculated based on the data provided.
5. **The slope 3/2 means that 2 inches of growth happens every 3 months.**
- **True**: A slope of 3/2 implies that for every 2 inches of growth, 3 months have passed (2 inches per 3 months).
6. **The equation of the line would be y = 3/2 x + 3 1/2.**
- **False**: While the slope is 3/2 (1.5), the y-intercept would be represented differently based on actual data points provided.
In summary, the statements that are TRUE based on the information given are:
- The slope 3/2 means that hair can grow 1.5 inches every month.
- The slope 3/2 means that 2 inches of growth happens every 3 months.