To solve the problem, let's follow these steps:
1. Determine the total number of miles the car can travel on a full tank:
- The average fuel economy of the car is 28 miles per gallon.
- The capacity of the fuel tank is 16 gallons.
- To find the total number of miles the car can travel with a full tank, simply multiply the fuel economy by the tank capacity:
[tex]\[
\text{Total miles} = 28 \, \text{miles/gallon} \times 16 \, \text{gallons} = 448 \, \text{miles}
\][/tex]
2. Formulate the function representing the remaining miles as fuel is consumed:
- Let \( y \) be the remaining miles the car can travel, and \( x \) be the number of gallons consumed.
- If the car starts with 448 miles worth of fuel, the miles left after consuming \( x \) gallons is given by:
[tex]\[
y = 448 - 28x
\][/tex]
- Here, \( 28x \) constitutes the miles already traveled (since 28 miles are traveled for each gallon), and subtracting this from the total gives the remaining distance.
3. Identify the correct option:
- The function we derived is:
[tex]\[
y = 448 - 28x
\][/tex]
- Comparing this with the provided options, we find that option C matches our derived function:
[tex]\[
\mathbf{C. \ } y=448-28x
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{C. \ y = 448 - 28x}
\][/tex]
