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​,404​) and ​(10​,488​). 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 471.2 feet above sea​ level?
Balloon Elevation
0
5
10
450
380
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 coordinates of this point are both 0.
D.
The​ y-coordinate of this point is always positive.

Answer 1

Part 1 — Select all that apply:
B. The y-coordinate of this point is the y-intercept.
(Options A, C, D are not generally true: A is not necessarily simpler in every case, C is only true for the origin, and D is false.)

Trend line:
Slope m = (488 − 404)/(10 − 0) = 84/10 = 8.4
Equation: y = 8.4x + 404

When y = 471.2:
471.2 = 8.4x + 404 → 8.4x = 67.2 → x = 8

So the balloon is at 471.2 ft after 8 minutes.