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​,474​) and ​(10​,563​). 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 527.4 feet above sea​ level?
Balloon Elevation
0
5
10
520
440
600
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.
The coordinates of this point are both 0.
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 17.8 x plus 474
y equals negative 17.8 x plus 474
B.y equals negative 8.9 x minus 474
y equals negative 8.9 x minus 474
C.y equals 8.9 x minus 474
y equals 8.9 x minus 474
D.y equals 8.9 x plus 474
y equals 8.9 x plus 474
Your answer is correct.
Part 3
After
  
enter your response here minutes the balloon is at an altitude of 527.4 feet above sea level.
​(Type an integer or a​ decimal.)

Answer 1

Part 1 — Why x = 0 is useful
- A: The y-coordinate is the y‑intercept. (True — the point with x = 0 gives the intercept.)
- D: It is easy to compute the slope using this point. (True — with (0,b) the slope m = (y2 − b)/(x2 − 0) simplifies the arithmetic.)

Part 2 — Trend line
The line through (0,474) and (10,563) has slope m = (563 − 474)/(10 − 0) = 89/10 = 8.9, so the equation is
y = 8.9x + 474.

Part 3 — When y = 527.4
Solve 527.4 = 8.9x + 474 → x = (527.4 − 474)/8.9 = 53.4/8.9 = 6.
The balloon is at 527.4 ft after 6 minutes.