Let's analyze the situation step-by-step:
1. Initial Amount: Jayne's tank already has 4 gallons of gasoline.
2. Gasoline Added: Let [tex]\( x \)[/tex] represent the number of gallons that Jayne puts into the tank during her stop.
3. Total Amount: The total amount of gasoline in the tank after adding [tex]\( x \)[/tex] gallons will be the sum of the initial amount and the amount added.
To find the correct equation, consider:
- The initial amount of gasoline in the tank is 4 gallons.
- When Jayne adds [tex]\( x \)[/tex] gallons, the total amount of gasoline [tex]\( y \)[/tex] in the tank can be written as the sum of 4 gallons (the initial amount) and [tex]\( x \)[/tex] gallons.
Thus, the relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] is:
[tex]\[ y = 4 + x \][/tex]
This equation clearly shows that the total amount of gasoline [tex]\( y \)[/tex] is equal to the initial 4 gallons plus the [tex]\( x \)[/tex] gallons that Jayne added.
So, the correct equation from the given options is:
[tex]\[ y = 4 + x \][/tex]
Let's review the provided options one by one:
- [tex]\( y = 4 + x \)[/tex]: This correctly represents the relationship.
- [tex]\( y = x - 4 \)[/tex]: This would imply that the total amount of gasoline in the tank is the number of gallons put in minus 4, which doesn't match the situation.
- [tex]\( y = 4 \cdot x \)[/tex]: This would imply that the total gasoline is 4 times the amount put in, which is incorrect in this context.
- [tex]\( y = x + 4 \)[/tex]: This is mathematically equivalent to [tex]\( y = 4 + x \)[/tex], but for clarity and consistency with provided choices, we will prefer [tex]\( y = 4 + x \)[/tex].
Therefore, the correct equation that relates the total amount of gasoline [tex]\( y \)[/tex] to the number of gallons [tex]\( x \)[/tex] that Jayne put in the tank is:
[tex]\[ y = 4 + x \][/tex]
