A leaf hangs from a branch 12 feet in the air. It falls to the ground at a rate of 0.25 feet per second. Which graph could represent the leaf’s height in feet as a function of time, in seconds, after leaving the branch?
Answers
Answer:
The correct answer is:
The last graph.
Explanation:
The leaf starts at 12 feet above the ground. This eliminates the first and third graph, leaving the second and last.
The leaf falls at 0.25 ft/sec. This means it would take 4 seconds for the leaf to fall 1 foot.
On the second graph, when we go over to 4 seconds and then up, the line is at 10 feet; this means it fell 2 feet in 4 seconds. This is too fast.
On the last graph, going over to 4 seconds and then up, the line is at 11 feet; this means it fell 1 foot in 4 seconds. This is correct.
I know this very well because I have read it
Graph is that of the straight line whose equation is y=12-0.25xy=12−0.25x
Step-by-step explanation:
- The equation of a straight line is given as y=mx+ cy = mx+ c
- In this case, y is the leaf's height in feet, x is the time in seconds, c is the initial height of 12 feet and m is the rate at which the leaf falls.
- Since the leaf is falling, the height is decreasing at the rate of 0.25 feet per second
- In this case, y=y= leaf's height in feet
m=-0.25m=−0.25
x=x= time in seconds
c=12c=12
- Therefore the graph is that of the straight line whose equation is y=12+(-0.25)*xy=12+(−0.25)∗x
- y=12-0.25xy=12−0.25x