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​,474​) and ​(10​,563​). 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 527.4 feet above sea​ level?
Balloon Elevation
0
5
10
520
440
600
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.
The coordinates of this point are both 0.
D.
It is easy to compute the slope using this point.

Answer 1

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

- A is true because a point with x = 0 gives the y-intercept.
- D is true because using x = 0 simplifies the slope calculation (you subtract 0).
- B is false (the y-value need not be positive).
- C is false (x = 0 does not imply y = 0 unless the point is the origin).

Trend line:
Slope m = (563 − 474)/(10 − 0) = 89/10 = 8.9, so the equation is
y = 8.9x + 474.

When y = 527.4:
527.4 = 8.9x + 474 → x = (527.4 − 474)/8.9 = 53.4/8.9 = 6.

The balloon is at 527.4 ft after 6 minutes.