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​,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.
Your answer is correct.B.
The coordinates of this point are both 0.
C.
It is easy to compute the slope using this point.
Your answer is correct.D.
The​ y-coordinate of this point is always positive.
Part 2
Which of these is a trend line for the data set​ shown? Use x to represent the number of minutes and y to represent the altitude of the balloon.
A.y equals 9.9 x plus 419
y equals 9.9 x plus 419
B.y equals negative 19.8 x plus 419
y equals negative 19.8 x plus 419
C.y equals 9.9 x minus 419
y equals 9.9 x minus 419
D.y equals negative 9.9 x minus 419
y equals negative 9.9 x minus 419

Answer 1

Part 1 — Select all that apply: A and C.
- A: A point with x = 0 gives the y-intercept (the constant term in the line).
- C: Using (0, y) makes slope computation easier because slope = (y2 − y1)/(x2 − 0) = y2/x2 when using the origin x = 0 point.

Part 2 — Trend line:
The slope = (518 − 419)/(10 − 0) = 99/10 = 9.9, so the equation is y = 9.9x + 419 (choice A).

When is y = 488.3?
Solve 488.3 = 9.9x + 419 → x = (488.3 − 419)/9.9 = 69.3/9.9 = 7 minutes.