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​,486​) and ​(10​,394​). 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 412.4 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.
The​ y-coordinate of this point is always positive.
B.
It is easy to compute the slope using this point.
C.
The​ y-coordinate of this point is the​ y-intercept.
D.
The coordinates of this point are both 0.

Answer 1

Part 1 — Select all that apply: B and C.
- B: True — using (0,y) makes slope calculation simpler: slope = (y2 − y0)/(x2 − 0).
- C: True — when x = 0 the y-value is the y‑intercept.
- A and D are false.

Trend line through (0,486) and (10,394):
- Slope m = (394 − 486)/(10 − 0) = −92/10 = −9.2
- Equation: y = −9.2x + 486

Solve for time when altitude y = 412.4:
412.4 = −9.2x + 486 → −9.2x = −73.6 → x = 8

So the balloon is at 412.4 ft after 8 minutes.