Question

hink 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​,419​) and ​(10​,518​). 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 488.3 feet above sea​ level?
Balloon Elevation
0
5
10
460
380
540
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 coordinates of this point are both 0.
C.
It is easy to compute the slope using this point.
D.
The​ y-coordinate of this point is always positive

Answer 1

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

- A is true: a point with x = 0 gives the y-intercept.
- C is true: using x = 0 often simplifies slope computation because one x-value is 0.
- B and D are false.

Trend line equation:
Slope m = (518 − 419)/(10 − 0) = 99/10 = 9.9, so y = 9.9x + 419.

Time to reach 488.3 ft:
488.3 = 9.9x + 419 ⇒ x = (488.3 − 419)/9.9 = 69.3/9.9 = 7 minutes.