Question

A balloon is released from the top of a building. The graph shows the height of the balloon over time. What does the slope and y-intercept reveal about the situation?
A. The balloon starts at a height of 100 ft and rises at a rate of 500 ft.
B. The balloon starts at a height of 0.5 ft and rises at a rate of 10 ft.
C. The balloon starts at a height of 500 ft and rises at a rate of 100 ft.

Answer 1

Given: Balloon is released from the top of a building.

To find: What does the slope and y-intercept reveal about the situation?

Solution:

• The graph given represents the height of the balloon with respect to time.

• Also from graph y-intercept represents height of the balloon (in thousand feet) at time equals zero is 0.5.

• Multiplying by 1000 to 0.5 as height of the balloon is given in thousand feet.

                  y intercept = 0.5 x 1000 = 500 feet

• So from this we can say that y-intercept represents the balloon starts from 500 feet.  

• Now we know that slope = y2-y1 / x2-x1

• So from graph we can assume that:

                 slope = 3.5 - 0.5 / 20

                           = 3 / 20

                           = 3 / 20 x 1000 = 150 feet.

So the slope is 150 feet which implies that the balloon starts at a height of 500 ft and rises at a rate of 150 ft.

Answer:

         The balloon starts at a height of 500 ft and rises at a rate of 150 ft.