Aleaf 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?

The rate is constant 0.25 feet/s and the initial position is 12 feet. then, the position equation is initial height - rate*time = y = 12 - 0.25t. this is the equation of a straight line with y-intercept 12, slope negative 0.25, t-intercept = 12/0.25 = 48s. with this information you can draw the graph easily.

Given that the rate is constant, you can predict that the function is linear and the graph is a straight line.the function is height, h(t) = 12 - 0.25t.now you can construct a table and use the pairs to make the graph: t                                h(t) = 12 - 0.25tseconds        feet0                              121                              12 - 0.25 = 11.752                              12 - 0.25(2) = 11.503                              12 - 0.25(3) = 11.254                              12 - 0.25(4) = 11.0010                          12 - 0.25(10) = 9.520                          12 - 0.25(20) = 7.040                         12 - 0.25(40) = 2.048                          12- 0.2(48) = 0so, you have plenty of points to draw the graph, which is a straight line from the point (0,12) to the point (48,0).