Im stuck on this question. A train travels along a straight track so that its distance in miles, d(t) , from Newark Penn Station is given as a function of time, t , in minutes. After 2 minutes the train has traveled 6 miles, and after 5 minutes the train has traveled 12 miles. Which of the following describes the slope of the relationship between t and d(t) ?
slope = ∆d/∆t = (12-6)/(5-2) = ___
speed during first 2 min = 6/2 = 3 miles/minute (no way by the way)
during next 3 min it does 6 miles again = 6/3 = 2 miles/min
It is slowing down. That is no surprise because 3 miles / min = 180 miles/hour which is a bit nuts just coming out of the station. Anyway negative slope.
To find the slope of the relationship between t and d(t), you need to use the formula for slope, which is:
slope = (change in y) / (change in x)
In this case, the "y" values are the distance traveled by the train, d(t), and the "x" values are the time in minutes, t.
Given that after 2 minutes the train has traveled 6 miles, and after 5 minutes it has traveled 12 miles, we can calculate the change in distance and time.
Change in distance = 12 miles - 6 miles = 6 miles
Change in time = 5 minutes - 2 minutes = 3 minutes
Now we can calculate the slope:
slope = (change in distance) / (change in time) = 6 miles / 3 minutes = 2 miles per minute
Therefore, the slope of the relationship between t and d(t) is 2 miles per minute.