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.
B.
The​ y-coordinate of this point is always positive.
C.
It is easy to compute the slope using this point.
D.
The coordinates of this point are both 0.

Answer 1

Part 1 — Select all that apply:
A and C.

- A is true because a point with x = 0 gives the y-intercept directly.
- C is true because using (0,y) makes the slope calculation simpler: slope = (y2 − y1)/(x2 − 0) = (y2 − y1)/x2.
- B and D are false.

Part 2 — Trend line equation:
Slope m = (392 − 475)/(10 − 0) = −83/10 = −8.3.
So the trend line is y = −8.3x + 475.

Part 3 — When is altitude 408.6 ft?
Solve 408.6 = −8.3x + 475 → −8.3x = −66.4 → x = 8.
The balloon is at 408.6 ft after 8 minutes.