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​,475​) and ​(10​,392​). 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 408.6 feet above sea​ level?
Balloon Elevation
0
5
10
430
360
500
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​ y-coordinate of this point is always positive.
C.
It is easy to compute the slope using this point.
Your answer is correct.D.
The coordinates of this point are both 0.
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 8.3 x minus 475
y equals 8.3 x minus 475
B.y equals negative 8.3 x minus 475
y equals negative 8.3 x minus 475
C.y equals 16.6 x plus 475
y equals 16.6 x plus 475
D.y equals negative 8.3 x plus 475
y equals negative 8.3 x plus 475

Answer 1

Part 1 — Select A and C.
- A: The y-coordinate at x = 0 is the y‑intercept.
- C: Using (0, y) makes slope calculation easy (rise/run from the intercept).

Part 2 — Trend line:
Points: (0,475) and (10,392). Slope = (392−475)/(10−0) = −83/10 = −8.3.
Equation: y = −8.3x + 475 (choice D).

When is y = 408.6?
408.6 = −8.3x + 475 → −8.3x = −66.4 → x = 8.
The balloon is at 408.6 ft after 8 minutes.