Question
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Several families are driving to an out-of-town soccer game. The table was used to create the scatter plot to show the distance each family drove and the time it took them.
Distance (mi)
126
137
124
130
134
113
119
145
128
138
110
142
Time (h)
1.9
2.1
2.0
2.0
2.3
1.8
2.0
2.3
2.1
2.2
1.7
2.2
Which equation best represents the line of fit?
Multiple choice question.
Disable choicecross out
A)
y = 0.071x+0.015
Disable choicecross out
B)
y = 0.015x+0.071
Disable choicecross out
C)
y = 0.071x−0.015
Disable choicecross out
D)
y = 0.015x−0.071
Part B
Fill in the blank question.
Use the line of fit to make a conjecture about the time it would take to drive 135 miles to the game. Round your answer to the nearest tenth. about
hours
Part A
Several families are driving to an out-of-town soccer game. The table was used to create the scatter plot to show the distance each family drove and the time it took them.
Distance (mi)
126
137
124
130
134
113
119
145
128
138
110
142
Time (h)
1.9
2.1
2.0
2.0
2.3
1.8
2.0
2.3
2.1
2.2
1.7
2.2
Which equation best represents the line of fit?
Multiple choice question.
Disable choicecross out
A)
y = 0.071x+0.015
Disable choicecross out
B)
y = 0.015x+0.071
Disable choicecross out
C)
y = 0.071x−0.015
Disable choicecross out
D)
y = 0.015x−0.071
Part B
Fill in the blank question.
Use the line of fit to make a conjecture about the time it would take to drive 135 miles to the game. Round your answer to the nearest tenth. about
hours
Answers
Answered by
GPT-4o mini
### Part A
To determine the equation that best represents the line of fit for the given data, we need to identify the relationship between distance (x) and time (y). Given the choices:
A) \(y = 0.071x + 0.015\)
B) \(y = 0.015x + 0.071\)
C) \(y = 0.071x - 0.015\)
D) \(y = 0.015x - 0.071\)
The appropriate relationship between distance and time (where time increases as distance increases) suggests that a model with a positive slope is correct.
Given that the distance range is from 110 to 145 miles and the time ranges from 1.7 to 2.3 hours, a slope of about 0.071 seems reasonable.
Thus, **A** likely represents the best fit because it maintains a positive slope.
### Correct Answer for Part A
**A)** \(y = 0.071x + 0.015\)
---
### Part B
To make a conjecture about the time it would take to drive 135 miles, we use the equation from Part A:
\[
y = 0.071(135) + 0.015
\]
Calculating this:
1. \(0.071 \times 135 = 9.585\)
2. Add \(0.015\):
\[
9.585 + 0.015 = 9.600
\]
So \(y \approx 9.600\) (which means about 1.6 hours).
Rounding this to the nearest tenth:
**About 1.6 hours.**
### Final Answer for Part B
1.6 hours
To determine the equation that best represents the line of fit for the given data, we need to identify the relationship between distance (x) and time (y). Given the choices:
A) \(y = 0.071x + 0.015\)
B) \(y = 0.015x + 0.071\)
C) \(y = 0.071x - 0.015\)
D) \(y = 0.015x - 0.071\)
The appropriate relationship between distance and time (where time increases as distance increases) suggests that a model with a positive slope is correct.
Given that the distance range is from 110 to 145 miles and the time ranges from 1.7 to 2.3 hours, a slope of about 0.071 seems reasonable.
Thus, **A** likely represents the best fit because it maintains a positive slope.
### Correct Answer for Part A
**A)** \(y = 0.071x + 0.015\)
---
### Part B
To make a conjecture about the time it would take to drive 135 miles, we use the equation from Part A:
\[
y = 0.071(135) + 0.015
\]
Calculating this:
1. \(0.071 \times 135 = 9.585\)
2. Add \(0.015\):
\[
9.585 + 0.015 = 9.600
\]
So \(y \approx 9.600\) (which means about 1.6 hours).
Rounding this to the nearest tenth:
**About 1.6 hours.**
### Final Answer for Part B
1.6 hours