Part A: The graph is linear. This is because all three lines in the graph are straight lines, indicating a constant rate of change between the x and y-values.
Part B:
- The graph is increasing in the segment from 0 to 2 seconds, as the distance from the hole increases from 0 to 9 centimeters.
- The graph is constant in the segment from 2 to 5 seconds, as the distance from the hole remains at 9 centimeters.
- The graph is decreasing in the segment from 5 to 7 seconds, as the distance from the hole decreases from 9 to 0 centimeters.
Part C: The motion of the ant can be described as follows:
- At the beginning, the ant moves away from the hole at a constant rate, covering 9 centimeters in 2 seconds.
- After that, the ant maintains a constant distance of 9 centimeters from the hole for a period of 3 seconds.
- Finally, the ant starts moving back towards the hole and reaches a distance of 0 centimeters in 7 seconds.
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:
A graph titled Motion of Ant is shown. The graph shows time in seconds on the x-axis and the Distance from Hole in centimeters on the y-axis. The scale on the x-axis is shown from 0 to 6 at increments of 1, and the scale on the y-axis is shown from 0 to 18 at increments of 3. The graph has 3 straight lines. The first line is labeled K and joins ordered pairs 0, 0 and 2, 9. The second line is labeled L and joins ordered pairs 2, 9 and 5, 9. The third line is labeled M and joins ordered pairs 5, 9 and 7, 0.
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)
1 answer
1 answer