Question
The table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground.
A 2-row table with 10 columns. The first row is labeled time (seconds), x with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.6. The second row is labeled height (meters), h with entries 100, 98.8, 95.1, 89.0, 80.4, 69.4, 55.9, 40.0, 21.6, 0.
A line of best fit for the data is represented by h = –21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table?
According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.
According to the line of best fit, the object was dropped from a lower height.
The line of best fit correctly predicts that the object reaches a height of 40 meters after 3.5 seconds.
The line of best fit predicts a height of 4 meters greater than the actual height for any time given in the table.
A 2-row table with 10 columns. The first row is labeled time (seconds), x with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.6. The second row is labeled height (meters), h with entries 100, 98.8, 95.1, 89.0, 80.4, 69.4, 55.9, 40.0, 21.6, 0.
A line of best fit for the data is represented by h = –21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table?
According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.
According to the line of best fit, the object was dropped from a lower height.
The line of best fit correctly predicts that the object reaches a height of 40 meters after 3.5 seconds.
The line of best fit predicts a height of 4 meters greater than the actual height for any time given in the table.
Answers
GPT-5 mini
The first statement is correct.
Set h = 0: 0 = −21.962x + 114.655 ⇒ x = 114.655/21.962 ≈ 5.22 s. The table shows the object hits the ground at 4.6 s, so the line predicts it about 5.22 − 4.6 ≈ 0.62 s (≈0.6 s) later.
(The other statements are false: the line’s intercept 114.655 > 100 so it predicts a higher drop height, at x = 3.5 the line gives ≈37.79 m (not 40), and the line’s error is not a constant 4 m.)
Set h = 0: 0 = −21.962x + 114.655 ⇒ x = 114.655/21.962 ≈ 5.22 s. The table shows the object hits the ground at 4.6 s, so the line predicts it about 5.22 − 4.6 ≈ 0.62 s (≈0.6 s) later.
(The other statements are false: the line’s intercept 114.655 > 100 so it predicts a higher drop height, at x = 3.5 the line gives ≈37.79 m (not 40), and the line’s error is not a constant 4 m.)