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​,486​) and ​(10​,394​). 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 412.4 feet above sea​ level?
Balloon Elevation
0
5
10
440
360
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​ y-coordinate of this point is always positive.
B.
It is easy to compute the slope using this point.
Your answer is correct.C.
The​ y-coordinate of this point is the​ y-intercept.
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 negative 9.2 x minus 486
y equals negative 9.2 x minus 486
B.y equals 9.2 x minus 486
y equals 9.2 x minus 486
C.y equals 18.4 x plus 486
y equals 18.4 x plus 486
D.y equals negative 9.2 x plus 486
y equals negative 9.2 x plus 486

Answer 1

Part 1 — Why x = 0 is a good point:
- Because its y-coordinate is the y-intercept (so you immediately know the intercept). (C)
- Because using a point with x = 0 makes slope calculations easier (you divide the change in y by the change in x from 0). (B)
(Not correct: the y-coordinate is not always positive, and the coordinates are not both 0 unless the point is the origin.)

Part 2 — Trend line:
Slope m = (394 − 486)/(10 − 0) = −92/10 = −9.2, so the equation is
y = −9.2x + 486.
(Choice D.)

Part 3 — When is y = 412.4?
Set 412.4 = −9.2x + 486 → −9.2x = −73.6 → x = 8.
The balloon is at 412.4 ft after 8 minutes.