Okay, here we have this:
Considering the provided information, we are going to find the required linear model, then we have:
So let us recall that a linear model has the following form: y=mx+b. Where b represents the intercept with the x axis, in our case it will be the initial distance. And m is the slope, that is, the change in distance per unit of time, therefore substituting we find the following function:
d=-900T+3000
Where d represents the distance traveled and T the hours of travel.
So now let's interpret the intercepts:
d-intercept: (0, 3000), This intercept tells us that when he started keeping track of the hours he was 3,000 kilometers from his point of arrival.
T-intercept: For this we are going to replace in the function with the distance equal to 0, to know how many hours it takes to reach its destination:
d=-900T+3000
0=-900T+3000
-900T=-3000
T=-3000/-900
T=10/3
So we have that the intercept with T is: (10/3, 0), and it represents that it will take 10/3 hours to reach its destination.
Finally let's identify the range and domain for our system:
Domain: Then the domain corresponds to the possible values that T can take, in this case it would be: [0, 10/3]. And it represents that time can only be taken from 0 to the moment they arrive.
Range: The range corresponds to all the possible values that the remaining distance can take, so we have: [0, 3000]. This means that the distance cannot be greater than 3000, nor less than 0.