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?

Answer 1

The equation of a straight line is given as $y=mx+c$

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:

$y=$ leaf's height in feet

$m=-0.25$

$x=$ time in seconds

$c=12$

Therefore the graph is that of the straight line whose equation is

$y=12+(-0.25)*x$

$y=12-0.25x$