Question

Think About the Process  Why is a data point with an​ x-coordinate of 0 a good point to use when creating a trend line for a data​ set? The graph shows the altitude of a weather balloon over time. The trend line passes through the points ​(0​,475​) and ​(10​,392​). Write the equation of a trend line for the data shown in the graph. After how many minutes is the balloon at an altitude of 408.6 feet above sea​ level?
Balloon Elevation
0
5
10
430
360
500
Time (min)
Altitude (ft)



x y graph
Question content area bottom
Part 1
Why is a data point with an​ x-coordinate of 0 a good point to use when creating a trend line for a data​ set? Select all that apply.
A.
The​ y-coordinate of this point is the​ y-intercept.
Your answer is correct.B.
The​ y-coordinate of this point is always positive.
C.
It is easy to compute the slope using this point.
Your answer is correct.D.
The coordinates of this point are both 0.
Part 2
Which of these is a trend line for the data set​ shown? Use x to represent the number of minutes and y to represent the altitude of the balloon.
A.y equals 8.3 x minus 475
y equals 8.3 x minus 475
Your answer is not correct.B.y equals negative 8.3 x minus 475
y equals negative 8.3 x minus 475
C.y equals 16.6 x plus 475
y equals 16.6 x plus 475
D.y equals negative 8.3 x plus 475
y equals negative 8.3 x plus 475
This is the correct answer.
Part 3
After
  
enter your response here minutes the balloon is at an altitude of 408.6 feet above sea level.
​(Type an integer or a​ decimal.)Think About the Process  Why is a data point with an​ x-coordinate of 0 a good point to use when creating a trend line for a data​ set? The graph shows the altitude of a weather balloon over time. The trend line passes through the points ​(0​,475​) and ​(10​,392​). Write the equation of a trend line for the data shown in the graph. After how many minutes is the balloon at an altitude of 408.6 feet above sea​ level?
Balloon Elevation
0
5
10
430
360
500
Time (min)
Altitude (ft)



x y graph
Question content area bottom
Part 1
Why is a data point with an​ x-coordinate of 0 a good point to use when creating a trend line for a data​ set? Select all that apply.
A.
The​ y-coordinate of this point is the​ y-intercept.
Your answer is correct.B.
The​ y-coordinate of this point is always positive.
C.
It is easy to compute the slope using this point.
Your answer is correct.D.
The coordinates of this point are both 0.
Part 2
Which of these is a trend line for the data set​ shown? Use x to represent the number of minutes and y to represent the altitude of the balloon.
A.y equals 8.3 x minus 475
y equals 8.3 x minus 475
Your answer is not correct.B.y equals negative 8.3 x minus 475
y equals negative 8.3 x minus 475
C.y equals 16.6 x plus 475
y equals 16.6 x plus 475
D.y equals negative 8.3 x plus 475
y equals negative 8.3 x plus 475
This is the correct answer.
Part 3
After
  
enter your response here minutes the balloon is at an altitude of 408.6 feet above sea level.
​(Type an integer or a​ decimal.)

Answer 1

Part 1 — Which apply?
- A. The y-coordinate is the y‑intercept. — Correct.
- C. It is easy to compute the slope using this point. — Correct.
(Reject B and D: the y‑coordinate need not be positive, and a point with x = 0 is not necessarily the origin.)

Part 2 — Trend line
Points: (0, 475) and (10, 392).
Slope = (392 − 475)/(10 − 0) = −83/10 = −8.3.
Equation: y = −8.3x + 475. (Option D.)

Part 3 — When is y = 408.6?
Solve 408.6 = −8.3x + 475
−8.3x = 408.6 − 475 = −66.4
x = −66.4 / −8.3 = 8

The balloon is at 408.6 ft after 8 minutes.