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.
Your answer is correct.D.
It is easy to compute the slope using this point.
Your answer is correct.
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 8.8 x plus 492
y equals negative 8.8 x plus 492
Your answer is correct.B.y equals 8.8 x minus 492
y equals 8.8 x minus 492
C.y equals 17.6 x plus 492
y equals 17.6 x plus 492
D.y equals negative 8.8 x minus 492
y equals negative 8.8 x minus 492
Part 3
After
  
enter your response here minutes the balloon is at an altitude of 412.8 feet above sea level.

Answer 1

Use the trend line y = -8.8x + 492. Set y = 412.8 and solve:

412.8 = -8.8x + 492
-8.8x = 412.8 - 492 = -79.2
x = -79.2 / -8.8 = 9

So the balloon is at 412.8 ft after 9 minutes.