Marc left his house to drive to work. He slowly pulls out of his driveway at a constant speed and continues at that speed until he slows and comes to a complete stop at the stop sign at the end of his street. He waits at the stop sign until it is his turn to go, and then his speed steadily increases until he reaches the speed limit. He drives at this constant speed until he approaches his office. He slows down steadily and comes to a complete stop in front of his office.



Which graph represents Marc’s drive to work?

Responses

Graph in the coordinate plane titled Marcs Drive to Work. The vertical is labeled speed in miles per hour. The horizontal axis is labeled time in minutes. There are six line segments on the graph. The first segment goes from begin ordered pair 0 comma 1 end ordered pair to begin ordered pair 1 comma 1 end ordered pair. The second segment goes from begin ordered pair 1 comma 1 end ordered pair to begin ordered pair 6 comma 7 end ordered pair. The third segment goes from begin ordered pair 6 comma 7 end ordered pair to begin ordered pair 11 comma 7 end ordered pair. The fourth segment goes from begin ordered pair 11 comma 7 end ordered pair to begin ordered pair 13 comma 5 end ordered pair. The fifth ordered pair goes from begin ordered pair 13 comma 5 end ordered pair to begin ordered pair 16 comma 5 end ordered pair. The sixth segment goes from begin ordered pair 16 comma 5 end ordered pair to begin ordered pair 19 comma 0 end ordered pair.
Image with alt text: Graph in the coordinate plane titled Marcs Drive to Work. The vertical is labeled speed in miles per hour. The horizontal axis is labeled time in minutes. There are six line segments on the graph. The first segment goes from begin ordered pair 0 comma 1 end ordered pair to begin ordered pair 1 comma 1 end ordered pair. The second segment goes from begin ordered pair 1 comma 1 end ordered pair to begin ordered pair 6 comma 7 end ordered pair. The third segment goes from begin ordered pair 6 comma 7 end ordered pair to begin ordered pair 11 comma 7 end ordered pair. The fourth segment goes from begin ordered pair 11 comma 7 end ordered pair to begin ordered pair 13 comma 5 end ordered pair. The fifth ordered pair goes from begin ordered pair 13 comma 5 end ordered pair to begin ordered pair 16 comma 5 end ordered pair. The sixth segment goes from begin ordered pair 16 comma 5 end ordered pair to begin ordered pair 19 comma 0 end ordered pair.

Graph in the coordinate plane titled Marcs Drive to Work. The vertical is labeled speed in miles per hour. The horizontal axis is labeled time in minutes. There are six line segments on the graph. The first segment goes from begin ordered pair 0 comma 2 end ordered pair to begin ordered pair 3 comma 2 end ordered pair. The second segment goes from begin ordered pair 3 comma 2 end ordered pair to begin ordered pair 5 comma 0 end ordered pair. The third segment goes from begin ordered pair 5 comma 0 end ordered pair to begin ordered pair 6 comma 0 end ordered pair. The fourth segment goes from begin ordered pair 6 comma 0 end ordered pair to begin ordered pair 10 comma 8 end ordered pair. The fifth ordered pair goes from begin ordered pair 10 comma 8 end ordered pair to begin ordered pair 16 comma 8 end ordered pair. The sixth segment goes from begin ordered pair 16 comma 8 end ordered pair to begin ordered pair 19 comma 0 end ordered pair.
Image with alt text: Graph in the coordinate plane titled Marcs Drive to Work. The vertical is labeled speed in miles per hour. The horizontal axis is labeled time in minutes. There are six line segments on the graph. The first segment goes from begin ordered pair 0 comma 2 end ordered pair to begin ordered pair 3 comma 2 end ordered pair. The second segment goes from begin ordered pair 3 comma 2 end ordered pair to begin ordered pair 5 comma 0 end ordered pair. The third segment goes from begin ordered pair 5 comma 0 end ordered pair to begin ordered pair 6 comma 0 end ordered pair. The fourth segment goes from begin ordered pair 6 comma 0 end ordered pair to begin ordered pair 10 comma 8 end ordered pair. The fifth ordered pair goes from begin ordered pair 10 comma 8 end ordered pair to begin ordered pair 16 comma 8 end ordered pair. The sixth segment goes from begin ordered pair 16 comma 8 end ordered pair to begin ordered pair 19 comma 0 end ordered pair.

Graph in the coordinate plane titled Marcs Drive to Work. The vertical is labeled speed in miles per hour. The horizontal axis is labeled time in minutes. There are six line segments on the graph. The first segment goes from begin ordered pair 0 comma 0 end ordered pair to begin ordered pair 4 comma 4 end ordered pair. The second segment goes from begin ordered pair 4 comma 4 end ordered pair to begin ordered pair 8 comma 4 end ordered pair. The third segment goes from begin ordered pair 8 comma 4 end ordered pair to begin ordered pair 11 comma 0 end ordered pair. The fourth segment goes from begin ordered pair 11 comma 0 end ordered pair to begin ordered pair 14 comma 6 end ordered pair. The fifth ordered pair goes from begin ordered pair 14 comma 6 end ordered pair to begin ordered pair 16 comma 6 end ordered pair. The sixth segment goes from begin ordered pair 16 comma 6 end ordered pair to begin ordered pair 19 comma 0 end ordered pair.
Image with alt text: Graph in the coordinate plane titled Marcs Drive to Work. The vertical is labeled speed in miles per hour. The horizontal axis is labeled time in minutes. There are six line segments on the graph. The first segment goes from begin ordered pair 0 comma 0 end ordered pair to begin ordered pair 4 comma 4 end ordered pair. The second segment goes from begin ordered pair 4 comma 4 end ordered pair to begin ordered pair 8 comma 4 end ordered pair. The third segment goes from begin ordered pair 8 comma 4 end ordered pair to begin ordered pair 11 comma 0 end ordered pair. The fourth segment goes from begin ordered pair 11 comma 0 end ordered pair to begin ordered pair 14 comma 6 end ordered pair. The fifth ordered pair goes from begin ordered pair 14 comma 6 end ordered pair to begin ordered pair 16 comma 6 end ordered pair. The sixth segment goes from begin ordered pair 16 comma 6 end ordered pair to begin ordered pair 19 comma 0 end ordered pair.

Graph in the coordinate plane titled Marcs Drive to Work. The vertical is labeled speed in miles per hour. The horizontal axis is labeled time in minutes. There are six line segments on the graph. The first segment goes from begin ordered pair 0 comma 0 end ordered pair to begin ordered pair 2 comma 4 end ordered pair. The second segment goes from begin ordered pair 2 comma 4 end ordered pair to begin ordered pair 5 comma 0 end ordered pair. The third segment goes from begin ordered pair 5 comma 0 end ordered pair to begin ordered pair 6 comma 0 end ordered pair. The fourth segment goes from begin ordered pair 6 comma 0 end ordered pair to begin ordered pair 10 comma 11 end ordered pair. The fifth ordered pair goes from begin ordered pair 10 comma 11 end ordered pair to begin ordered pair 15 comma 11 end ordered pair. The sixth segment goes from begin ordered pair 15 comma 11 end ordered pair to begin ordered pair 19 comma 0 end ordered pair.

1 answer

To analyze which graph best represents Marc's drive to work, let's break down his journey into different phases based on the description:

  1. Pulling out of the driveway: Marc starts from rest and slowly increases his speed as he pulls out. This indicates a slow acceleration over a short period.

  2. Coming to a complete stop at the stop sign: Marc maintains the same, low speed until he stops at the stop sign. This phase will appear as a horizontal line on the graph, indicating constant low speed, followed by a drop to 0 mph as he comes to a stop.

  3. Waiting at the stop sign: During the wait, the speed is 0 mph, appearing as a flat line at the bottom of the graph.

  4. Accelerating to the speed limit: After the stop sign, Marc steadily increases his speed until he reaches the speed limit. This phase will show a steady, upward slope on the graph as the speed increases.

  5. Driving at constant speed: Once he reaches the speed limit, his speed remains constant for a while, indicated by another horizontal line.

  6. Slowing down to stop in front of the office: As he approaches his office, he slows down steadily and comes to a complete stop. This will appear as a downward slope on the graph leading to 0 mph at the end.

Based on these points, we should look for a graph that has these characteristics:

  • A starting point of low speed gradually increasing to a higher speed.
  • Flat sections representing constant low speed and then constant high speed.
  • Downslopes leading back down to 0 before the end.

Among the provided graphs, the one that captures this sequence effectively is:

Graph 1:

  1. Starts from a low speed and increases (0 to 1, then to 7).
  2. Flat segment reflecting constant speed at 7 mph until around time 11.
  3. Decrease to 0 after time 16.

Thus, Graph 1 accurately represents Marc's drive to work.