The final last graph is the correct option.
The problem describes a scenario where Myiah rides her bike from home to the park to meet a friend, then sits and talks, and finally rides back home at a slower rate. To determine which graph represents this situation, let's break down the steps that should be reflected in the graph:
1. Myiah riding to the park: This part of the graph should show a line moving away from the origin, indicating increasing distance from home as time passes. The slope of this line should be constant, showing a steady rate of travel.
2. Myiah sitting at the park: During this time, the distance from home does not change, so the graph should show a horizontal line, indicating that time is passing but the distance remains constant.
3. Myiah riding home: For this part, the graph should show a line moving back towards the origin, indicating a decreasing distance from home as time passes. Since she's riding back at a slower rate, this line should have a shallower slope than the line representing the trip to the park.
Now let's analyze the options given:
- The first graph shows a line moving away from the origin, then a horizontal line, and finally a line moving back towards the origin at a shallower slope. This matches the description of the situation.
- The second graph shows a consistent slope away from the origin and then back towards it without a horizontal section, which would suggest no time spent sitting at the park.
- The third graph seems to show an initial distance from home that decreases and then increases, which does not match the description of Myiah starting at home.
Based on the steps and description provided, the first graph would be the correct representation of the situation. It shows an initial period of travel with a steady slope, a period of no change in distance representing the time spent sitting and talking, and a final period of travel with a shallower slope representing the slower ride home.