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​,492​) and ​(10​,404​). 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 412.8 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.
The coordinates of this point are both 0.
B.
The​ y-coordinate of this point is always positive.
C.
The​ y-coordinate of this point is the​ y-intercept.
D.
It is easy to compute the slope using this point.

Answer 1

Part 1 — select all that apply:
C and D.
- C: A point with x = 0 gives the y-intercept.
- D: Using the x = 0 point makes slope calculation easier (slope = (other y − y at x=0)/(other x)).

Trend line:
Slope m = (404 − 492)/(10 − 0) = −88/10 = −8.8, so
y = −8.8x + 492.

When y = 412.8:
412.8 = −8.8x + 492 ⇒ −8.8x = −79.2 ⇒ x = 9.
The balloon is at 412.8 ft after 9 minutes.