Jillian walked 0.5 miles before she started jogging at an average pace of 5 miles per hour. The equation d = 0.5 5t can be used to relate the total distance, d, in miles to the time, t, that Jillian spent jogging. What are the independent and dependent variables?

Recall what independent/dependent variables are. In the current function, wouldn't you agree that time is the determining factor for finding out how many miles Jillian jogged? That's the independent variable, as time can be any interval from [0,infinity). Now the dependent variable happens to be what the outcome that occurs because of the independent variable. As we've found, time is the independent variable, and for any t value that is plugged into the equation, you find that distance is being changed as a result of time. Thus, distance is the dependent variable.