Final answer:
Without specific details about Manuel's running speed, any of the given linear equations could represent his running distance over time. If the example jogger's average velocity of 4.00 m/s is comparable, then Option 1: y=4x might be a potential match.
Step-by-step explanation:
The student is asking which function could represent Manuel's running distance over time. In the context of the question, the distance is proportional to the time, suggesting a linear relationship between the two variables. This means we are looking for a linear equation of the form y = mx, where 'y' represents the distance run and 'x' represents time. Since we don't have specific values to determine the rate at which Manuel runs, we cannot definitively select one of the options as the correct function without additional context. However, if the rate at which the jogger from Example 2.8 is relevant, then Option 1: y=4x might be a possible match since it mirrors the jogger's average velocity of 4.00 m/s. Without further information regarding Manuel's running speed or conditions, any of the given linear options could represent his running distance over time, assuming 'x' is the time in the same units as Manuel's running speed.