Let's walk through the problem step-by-step to find the equation that correctly represents the total amount of gasoline in Jayne's tank.
1. Understand the given information:
- The tank already has 4 gallons of gas in it.
2. Determine what is being asked:
- We need to establish an equation that relates the total amount of gasoline in the tank (denoted by [tex]\( y \)[/tex]) to the number of gallons that Jayne puts into the tank (denoted by [tex]\( x \)[/tex]).
3. Formulate the equation:
- The total amount of gasoline [tex]\( y \)[/tex] is the sum of the initial amount of gas and the additional gallons put in.
4. Understand the initial amount of gasoline:
- Jayne starts with 4 gallons of gas in the tank. So, the initial amount is 4 gallons.
5. Express the relationship:
- If Jayne puts in [tex]\( x \)[/tex] gallons more, the total amount of gasoline [tex]\( y \)[/tex] will be the initial 4 gallons plus the [tex]\( x \)[/tex] gallons added.
6. Write the equation:
- Therefore, the equation relating [tex]\( y \)[/tex] (the total amount of gasoline in the tank) to [tex]\( x \)[/tex] (the number of gallons added) is:
[tex]\[
y = 4 + x
\][/tex]
Checking other options:
- Option 2: [tex]\( y = x - 4 \)[/tex]. This would imply that the total amount of gas is less than the amount added by 4 gallons, which does not make sense given the initial information.
- Option 3: [tex]\( y = 4 \cdot x \)[/tex]. This would imply a multiplicative relationship, which is incorrect because adding gasoline is an additive process, not a multiplicative one.
- Option 4: [tex]\( y = x + 4 \)[/tex]. This is just a rewritten form of [tex]\( y = 4 + x \)[/tex] because addition is commutative, i.e., [tex]\( 4 + x \)[/tex] is the same as [tex]\( x + 4 \)[/tex].
Thus, the correct equation is indeed [tex]\( y = 4 + x \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{y = 4 + x} \][/tex]
