On the way to the mall Miguel rides his skateboard to get to the bus stop. He then waits a few minutes for the bus to come, then rides the bus to the mall. He gets off the bus when it stops at the mall and walks across the parking lot to the closest entrance. Which graph correctly models his travel time and distance?

Question

A graph has time on the x-axis and distance on the y-axis. The graph increases, increases rapidly, is constant, increases, and then decreases to a distance of 0.
A graph has time on the x-axis and distance on the y-axis. The graph increases, increases rapidly, is constant, increases, and then is constant.
A graph has time on the x-axis and distance on the y-axis. The graph increases, is constant, increases, is constant, and then increases slightly.
A graph has time on the x-axis and distance on the y-axis. The graph increases, is constant, increases rapidly, increases, and then increases slowly.

Answer 1

To model Miguel's travel time and distance accurately, let's break down his journey:

1. Skateboarding to the bus stop: This part involves accelerating and moving quickly. The graph would start at the origin (0,0) and show an increasing line as he rides.

2. Waiting for the bus: When he waits, the distance remains constant while time passes, leading to a horizontal line on the graph.

3. Riding the bus to the mall: He will travel a significant distance while on the bus, which typically occurs at a faster pace than skateboarding, so this part of the graph will also show an increasing line, likely at a steeper slope than when he skateboarded.

4. Walking across the parking lot: This part will again show an increase in distance as he reaches the mall entrance.

In summary, the phases of his journey would be:

• Increase (skateboarding)
• Constant (waiting for the bus)
• Increase (riding the bus)
• Increase (walking to the entrance)

Among the given options, the graph that fits this description is:

A graph has time on the x-axis and distance on the y-axis. The graph increases, is constant, increases, is constant, and then increases slightly.

This choice captures all the phases of Miguel's journey, including the waiting period and the walking after getting off the bus at the mall.