Tina is going for a bike ride. When she leaves her house, she starts pedaling and her speed steadily increases for a while. Then she coasts for a while at a constant speed before she starts pedaling again, and her speed steadily increases again at a slower rate than it did before. When her legs get tired, she coasts at a constant speed again. Finally, she reaches her destination and her speed steadily decreases until she comes to a complete stop.



Which graph represents Tina’s bike ride?

Responses

Graph in the coordinate plane titled Tinas bike ride. 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 3 comma 6 end ordered pair. The second segment goes from begin ordered pair 3 comma 6 end ordered pair to begin ordered pair 7 comma 6 end ordered pair. The third segment goes from begin ordered pair 6 comma 6 end ordered pair to begin ordered pair 12 comma 10 end ordered pair. The fourth segment goes from begin ordered pair 12 comma 10 end ordered pair to begin ordered pair 16 comma 10 end ordered pair. The fifth ordered pair goes from begin ordered pair 16 comma 10 end ordered pair to begin ordered pair 19 comma 0 end ordered pair.
Image with alt text: Graph in the coordinate plane titled Tinas bike ride. 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 3 comma 6 end ordered pair. The second segment goes from begin ordered pair 3 comma 6 end ordered pair to begin ordered pair 7 comma 6 end ordered pair. The third segment goes from begin ordered pair 6 comma 6 end ordered pair to begin ordered pair 12 comma 10 end ordered pair. The fourth segment goes from begin ordered pair 12 comma 10 end ordered pair to begin ordered pair 16 comma 10 end ordered pair. The fifth ordered pair goes from begin ordered pair 16 comma 10 end ordered pair to begin ordered pair 19 comma 0 end ordered pair.

Graph in the coordinate plane titled Tinas bike ride. 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 5 comma 4 end ordered pair. The second segment goes from begin ordered pair 5 comma 4 end ordered pair to begin ordered pair 9 comma 4 end ordered pair. The third segment goes from begin ordered pair 9 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 12 comma 0 end ordered pair. The fifth ordered pair goes from begin ordered pair 12 comma 0 end ordered pair to begin ordered pair 14 comma 8 end ordered pair. The sixth segment goes from begin ordered pair 14 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 Tinas bike ride. 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 5 comma 4 end ordered pair. The second segment goes from begin ordered pair 5 comma 4 end ordered pair to begin ordered pair 9 comma 4 end ordered pair. The third segment goes from begin ordered pair 9 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 12 comma 0 end ordered pair. The fifth ordered pair goes from begin ordered pair 12 comma 0 end ordered pair to begin ordered pair 14 comma 8 end ordered pair. The sixth segment goes from begin ordered pair 14 comma 8 end ordered pair to begin ordered pair 19 comma 0 end ordered pair.

Graph in the coordinate plane titled Tinas bike ride. 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 3 comma 8 end ordered pair. The second segment goes from begin ordered pair 3 comma 8 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 7 comma 0 end ordered pair. The fourth segment goes from begin ordered pair 7 comma 0 end ordered pair to begin ordered pair 11 comma 4 end ordered pair. The fifth ordered pair goes from begin ordered pair 11 comma 4 end ordered pair to begin ordered pair 15 comma 4 end ordered pair. The sixth segment goes from begin ordered pair 15 comma 4 end ordered pair to begin ordered pair 19 comma 0 end ordered pair.
Image with alt text: Graph in the coordinate plane titled Tinas bike ride. 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 3 comma 8 end ordered pair. The second segment goes from begin ordered pair 3 comma 8 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 7 comma 0 end ordered pair. The fourth segment goes from begin ordered pair 7 comma 0 end ordered pair to begin ordered pair 11 comma 4 end ordered pair. The fifth ordered pair goes from begin ordered pair 11 comma 4 end ordered pair to begin ordered pair 15 comma 4 end ordered pair. The sixth segment goes from begin ordered pair 15 comma 4 end ordered pair to begin ordered pair 19 comma 0 end ordered pair.

Graph in the coordinate plane titled Tinas bike ride. 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 7 end ordered pair. The second segment goes from begin ordered pair 4 comma 7 end ordered pair to begin ordered pair 7 comma 2 end ordered pair. The third segment goes from begin ordered pair 7 comma 2 end ordered pair to begin ordered pair 10 comma 2 end ordered pair. The fourth segment goes from begin ordered pair 10 comma 2 end ordered pair to begin ordered pair 13 comma 7 end ordered pair. The fifth ordered pair goes from begin ordered pair 13 comma 7 end ordered pair to begin ordered pair 15 comma 7 end ordered pair. The sixth segment goes from begin ordered pair 15 comma 7 end ordered pair to begin ordered pair 19 comma 0 end ordered pair.

1 answer

To determine which graph represents Tina's bike ride based on her described behavior:

  1. Starts pedaling and speed increases steadily: This should be represented by an upward slope on the graph.
  2. Coasts at a constant speed: This will appear as a horizontal line segment at a consistent speed.
  3. Starts pedaling again with a slower increase in speed: This indicates another upward slope, but not as steep as the first.
  4. Coasts again at constant speed: Another horizontal line segment at a new constant speed.
  5. Final decrease in speed until stopping: This should be a downward slope leading back to zero speed.

From your descriptions of the graphs:

  1. The first graph shows:

    • Speed increasing from (0,0) to (3,6) (upward slope).
    • Constant speed from (3,6) to (7,6) (horizontal).
    • An increase from (7,6) to (12,10) (upward slope, but now at a higher speed).
    • Constant speed from (12,10) to (16,10) (horizontal).
    • Finally decreasing from (16,10) to (19,0) (downward slope).

    This graph matches Tina's behavior well, especially with the two phases of constant speed and the increase in speed again.

  2. The second graph doesn't have a second increase in speed after coasting. It goes directly to a stop after a different pattern which doesn't match the description.

  3. The third graph shows an initial increase but then a stop, not a second increase in speed, which also doesn't capture the complete behavior.

  4. The fourth graph presents a combination that doesn't match the description either, as it incorrectly shows increases and decreases without proper coasting.

Therefore, the first graph best represents Tina's bike ride with all characteristics matching her speed changes accurately.