Answer:
For train A, the distance traveled as a function of time in hours is written as:
y = 68*x
For train B, we know that it's equation passes through the points (0, 0) and (1, 64)
Remember that:
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Then the slope for the equation of train B is:
a = (64 - 0)/(1 - 0) = 64
Then equation of train B is something like:
y = 64*x + b
Now, we know that it passes through the point (0, 0), this means that when x = 0, we also have y = 0, then if we replace these two values in the equation we get:
0 = 64*0 + b
0 = 0 +b
then b = 0
This means that the equation for train B is:
y = 64*x
Where again, y is the distance in miles and x is the time in hours.
If we look at both equations, we can see that train A has a larger slope, which means that for each unit of time, train A travels a larger distance, then we can conclude that train A is faster than train B.
