Question

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?

A coordinate plane showing Falling Leaf, Time in seconds on the x-axis and Height in feet on the y-axis. A line is passing through (4, 20 ), (6, 14), and (12, 0).

A coordinate plane showing Falling Leaf, Time in seconds on the x-axis and Height in feet on the y-axis. A line is passing through (0, 12), (8, 8), and (20, 2).

A coordinate plane showing Falling Leaf, Time in seconds on the x-axis and Height in feet on the y-axis. A line is passing tt


A coordinate plane showing Falling Leaf, Time in seconds on the x-axis and Height in feet on the y-axis. A line is passing through (4, 20 ), (6, 14), and (12, 0).

A coordinate plane showing Falling Leaf, Time in seconds on the x-axis and Height in feet on the y-axis. A line is passing through (0, 12), (8, 8), and (20, 2).

A coordinate plane showing Falling Leaf, Time in seconds on the x-axis and Height in feet on the y-axis. A line is passing through (0, 16), (6, 8), and (12, 0).

A coordinate plane showing Falling Leaf, Time in seconds on the x-axis and Height in feet on the y-axis. A line is passing through (0, 12), (8, 10), and (16, 8).hrough (0, 16), (6, 8), and (12, 0).

Answer 1

Height h(t) = 12 − 0.25t (starts at 12 ft and decreases 0.25 ft/s), so the graph must be a line through (0,12) with slope −0.25. The line through (0,12), (8,10), (16,8) has slope (10−12)/(8−0)=−2/8=−0.25, so that graph is correct.