As part of a science experiment, Natasha drops a bouncy ball from various heights, h, and observes the height to which the ball rebounds, r. The table shows the results of Natasha's experiment.
Initial height, h (in meters) Rebound height, r (in meters)
0.30 0.21
0.50 0.35
0.80 0.56
1.00 0.7
1.20 0.84
Which equation represents the proportional relationship between the initial height and the rebound height of the bouncy ball?
A.
B.
C.
D.
To find the equation representing the proportional relationship between the initial height and the rebound height of the bouncy ball, we need to determine the constant ratio between the two variables. This can be done by dividing the rebound height by the initial height for each data point.
For the given data:
0.21/0.30 ≈ 0.7
0.35/0.50 ≈ 0.7
0.56/0.80 ≈ 0.7
0.7/1.00 = 0.7
0.84/1.20 ≈ 0.7
Since the ratio between the rebound height and the initial height is approximately 0.7 for all the data points, the equation representing the proportional relationship is:
r = 0.7h
Therefore, the correct equation is:
A. r = 0.7h