Need on this question

the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds:

a linear model with ordered pairs at 0, 60 and 2, 80 and 3, 80 and 4, 20 and 6, 0 and 7, 0 and 8, 0. the x axis is labeled time in seconds, and the y axis is labeled height in feet.

part a: during what interval(s) of the domain is the water balloon's height increasing?

part b: during what interval(s) of the domain is the water balloon's height staying the same?

part c: during what interval(s) of the domain is the water balloon's height decreasing the fastest? use complete sentences to support your answer.

part d: use the constraints of the real-world situation to predict the height of the water balloon at 10 seconds. use complete sentences to support your answer.

Part A) Interval [0,2]

Part B) Interval [2,3] and [6,8]

Part C) In the interval [3,4] the water balloon's height decreasing the fastest

Part D) The water balloon's height at 10 seconds is equal to zero

Step-by-step explanation:

Part A: During what interval(s) of the domain is the water balloon's height increasing?

see the attached figure to better understand the problem

During the interval [0,2] the height of the water balloon is increasing

All real numbers greater than or equal to 0 seconds and less than or equal to 2 seconds

The slope of the linear equation in that interval is positive

Part B: During what interval(s) of the domain is the water balloon's height staying the same?

Looking at the graph

During the interval [2,3]  and [6,8] the water balloon's height is the same

The slope of the linear equation in that intervals is equal to zero ( is a horizontal line)

Part C: During what interval(s) of the domain is the water balloon's height decreasing the fastest?

Determine the slope

The formula to calculate the slope between two points is equal to

Interval [3,4]

For x= 3 sec ----> h=80 ft

For x= 4 sec ----> h=20 ft

substitute

Interval [4,6]

For x= 4 sec ----> h=20 ft

For x= 6 sec ----> h=0 ft

substitute

therefore

In the interval [3,4] the water balloon's height decreasing the fastest, because the graph has the steepest negative slope

Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 10 seconds

Looking at the graph

During the interval [6,8]

The water balloon's height at 10 seconds is equal to zero, because the water balloon hit the ground at x=6 sec

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

x/3-10=8

x/3=18

x=48