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​,488​) and ​(10​,395​). 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 404.3 feet above sea​ level?
Balloon Elevation
0
5
10
440
360
520
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.
It is easy to compute the slope using this point.
Your answer is correct.B.
The​ y-coordinate of this point is the​ y-intercept.
Your answer is correct.C.
The​ y-coordinate of this point is always positive.
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 18.6 x plus 488
y equals 18.6 x plus 488
B.y equals negative 9.3 x minus 488
y equals negative 9.3 x minus 488
C.y equals negative 9.3 x plus 488
y equals negative 9.3 x plus 488
Your answer is correct.D.y equals 9.3 x minus 488
y equals 9.3 x minus 488
Part 3
After
  
enter your response here minutes the balloon is at an altitude of 404.3 feet above sea level.
​(Type an integer or a​ decimal.)

Answer 1

Part 1 — why x = 0 is a good point:
- A (true): using (0,b) makes slope calculation straightforward.
- B (true): the y-coordinate at x = 0 is the y‑intercept.
- C (false): the y‑coordinate at x = 0 need not be positive.
- D (false): the coordinates are not both 0 unless the point is the origin.

Part 2 — trend line:
The slope m = (395 − 488)/(10 − 0) = −93/10 = −9.3, and the y‑intercept is 488.
Equation: y = −9.3x + 488.

Part 3 — when y = 404.3:
404.3 = −9.3x + 488
−9.3x = 404.3 − 488 = −83.7
x = (−83.7)/(−9.3) = 9

So the balloon is at 404.3 ft after 9 minutes.