The distance, y, in centimeters, of an ant from a hole in the tree for a certain amount of time, x, in seconds, is shown in the graph: part a: is the graph linear or nonlinear? explain your answer. (2 points) part b: in which segments is the graph increasing, decreasing, and constant? (3 points) part c: in your own words, describe the motion of the ant, as shown on the graph. (5 points)

A.  Non linear

B  The graph is increasing over the region from 0 to 2.  The graph is decreasing from 4 to 6. The graph is constant from 2 to 4.  

C. The ant leaves his hole at 0 seconds and starts walking away from the hole until 2 seconds.  He stops and waits until 4 seconds.  He then starts walking back to his hole at the same speed  until 6 seconds  when he is at his hole.

Step-by-step explanation:

Part A:  Is this graph linear or non linear?

A linear graph is a straight line.  This graph is piecewise linear, but is not a straight line over the entire region.  Therefore this graph is not linear.

Part B:  

The graph is increasing over the region from 0 to 2.  The slope is increasing during that time.  The graph is decreasing from 4 to 6.  The slope is decreasing during that time.  The graph is constant from 2 to 4.  The slope is 0 during that time.

Part C

The ant leaves his hole at 0 seconds and starts walking away from the hole until 2 seconds.  He stops and waits until 4 seconds.  He then starts walking back to his hole at the same speed  until 6 seconds  when he is at his hole.