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.
B.
The​ y-coordinate of this point is the​ y-intercept.
C.
The​ y-coordinate of this point is always positive.
D.
The coordinates of this point are both 0.

Answer 1

Part 1 — Select all that apply:
A and B.
- A: having x = 0 makes the slope formula simpler (denominator or subtraction involves 0).
- B: the y-value at x = 0 is the y‑intercept.

Equation of trend line:
Slope m = (395 − 488)/(10 − 0) = −93/10 = −9.3, so
y = −9.3x + 488.

When is altitude 404.3 ft?
Solve 404.3 = −9.3x + 488 → −9.3x = −83.7 → x = 9.
The balloon is at 404.3 ft after 9 minutes.