For this case we have that the relationship is direct.
Therefore, we have:
![y = k * x](https://tex.z-dn.net/?f=%20y%20%3D%20k%20%2A%20x%20%20)
Where,
y: distance traveled in kilometers
x: number of liters of fuel
k: proportionality constant
We must look for the value of k. For this, we use the following data:
This car can travel 476 kilometers on 17 liters of fuel.
Substituting values we have:
![476 = k * 17](https://tex.z-dn.net/?f=%20476%20%3D%20k%20%2A%2017%20%20)
From here, we clear the value of k:
![k = \frac{476}{17}\\k = 28](https://tex.z-dn.net/?f=%20k%20%3D%20%5Cfrac%7B476%7D%7B17%7D%5C%5Ck%20%3D%2028%20%20%20)
Therefore, the relationship is:
![y = 28x](https://tex.z-dn.net/?f=%20y%20%3D%2028x%20%20)
For 1428 kilometers we have:
![1428 = 28x](https://tex.z-dn.net/?f=%201428%20%3D%2028x%20%20)
Clearing the amount of fuel we have:
![x = \frac{1428}{28}\\x = 51](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cfrac%7B1428%7D%7B28%7D%5C%5Cx%20%3D%2051%20%20%20)
Answer:
51 liters of fuel are required for the vehicle to travel 1,428 kilometers