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 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 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 = 3/2 x + 3 1/2
The equation of the line would be y = 3/2 x + 3 1/2
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 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
Months of growth
3
5
8
9
15
Length of hair (inches)
8
11
15.5
17
26
(3 points)
Responses
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 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 = 3/2 x + 3 1/2
The equation of the line would be y = 3/2 x + 3 1/2
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 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
Answers
GPT-4o mini
To determine which statements are true, let's analyze the provided data. We have the following relationship between the months of growth and the length of hair in inches:
- Months of growth: 3, 5, 8, 9, 15
- Length of hair (inches): 8, 11, 15.5, 17, 26
First, we can try to find the slope of the linear relationship representing hair growth.
1. **Calculate the growth rate (slope)**. Using the length of hair data:
- Change in length when going from 3 months (8 inches) to 5 months (11 inches): 11 - 8 = 3 inches over 5 - 3 = 2 months.
- Change in length when going from 5 months (11 inches) to 8 months (15.5 inches): 15.5 - 11 = 4.5 inches over 8 - 5 = 3 months.
- Change in length when going from 8 months (15.5 inches) to 9 months (17 inches): 17 - 15.5 = 1.5 inches over 9 - 8 = 1 month.
- Change in length when going from 9 months (17 inches) to 15 months (26 inches): 26 - 17 = 9 inches over 15 - 9 = 6 months.
From these calculations, it would be beneficial to find the average growth rate. Overall growth from 3 months to 15 months is:
- Total growth from 8 inches to 26 inches = 26 - 8 = 18 inches.
- Total time from 3 months to 15 months = 15 - 3 = 12 months.
- Average growth rate (slope) = Total growth / Total time = 18 inches / 12 months = 1.5 inches per month.
Now let's go through the statements one-by-one:
1. **The equation of the line would be y = 3.5 x + 3/2.**
- False. The slope calculated is 1.5 (or 3/2), not 3.5.
2. **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 is not correctly represented; it should be related to hair growth at month 0.
3. **The equation of the line would be y = 3/2 x + 3 1/2.**
- False. While the slope of the line is indeed 3/2, the y-intercept values do not fit; for example, at 0 months, we calculate y using previous data.
4. **The slope 3/2 means that 2 inches of growth happens every 3 months.**
- False. The slope 3/2 means that 1.5 inches of growth happens every month, not every 3 months.
5. **The slope 3/2 means that hair can grow 1.5 inches every month.**
- True. This statement is indeed confirmed by calculation.
6. **The y-intercept (0, 3.5) means that at the starting time, there was 3.5 inches of hair.**
- False. An accurate equation should be derived for the intercept; based on data, we cannot confirm the value of the intercept.
Based on the analysis, the only true statement is:
- **The slope 3/2 means that hair can grow 1.5 inches every month.**
- Months of growth: 3, 5, 8, 9, 15
- Length of hair (inches): 8, 11, 15.5, 17, 26
First, we can try to find the slope of the linear relationship representing hair growth.
1. **Calculate the growth rate (slope)**. Using the length of hair data:
- Change in length when going from 3 months (8 inches) to 5 months (11 inches): 11 - 8 = 3 inches over 5 - 3 = 2 months.
- Change in length when going from 5 months (11 inches) to 8 months (15.5 inches): 15.5 - 11 = 4.5 inches over 8 - 5 = 3 months.
- Change in length when going from 8 months (15.5 inches) to 9 months (17 inches): 17 - 15.5 = 1.5 inches over 9 - 8 = 1 month.
- Change in length when going from 9 months (17 inches) to 15 months (26 inches): 26 - 17 = 9 inches over 15 - 9 = 6 months.
From these calculations, it would be beneficial to find the average growth rate. Overall growth from 3 months to 15 months is:
- Total growth from 8 inches to 26 inches = 26 - 8 = 18 inches.
- Total time from 3 months to 15 months = 15 - 3 = 12 months.
- Average growth rate (slope) = Total growth / Total time = 18 inches / 12 months = 1.5 inches per month.
Now let's go through the statements one-by-one:
1. **The equation of the line would be y = 3.5 x + 3/2.**
- False. The slope calculated is 1.5 (or 3/2), not 3.5.
2. **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 is not correctly represented; it should be related to hair growth at month 0.
3. **The equation of the line would be y = 3/2 x + 3 1/2.**
- False. While the slope of the line is indeed 3/2, the y-intercept values do not fit; for example, at 0 months, we calculate y using previous data.
4. **The slope 3/2 means that 2 inches of growth happens every 3 months.**
- False. The slope 3/2 means that 1.5 inches of growth happens every month, not every 3 months.
5. **The slope 3/2 means that hair can grow 1.5 inches every month.**
- True. This statement is indeed confirmed by calculation.
6. **The y-intercept (0, 3.5) means that at the starting time, there was 3.5 inches of hair.**
- False. An accurate equation should be derived for the intercept; based on data, we cannot confirm the value of the intercept.
Based on the analysis, the only true statement is:
- **The slope 3/2 means that hair can grow 1.5 inches every month.**