To determine if the equation \(3x + 4 = y\) represents a direct proportion, we need to see if it can be written in the form \(y = kx\), where \(k\) is a constant. This form signifies that \(y\) is directly proportional to \(x\).
Let's solve the equation for \(y\):
1. Start with the given equation:
[tex]\[
3x + 4 = y
\][/tex]
2. Our goal is to express \(y\) in terms of \(x\) in a simplified form:
[tex]\[
y = 3x + 4
\][/tex]
Now, we observe the form of the equation \(y = 3x + 4\). For an equation to represent a direct proportion, it must be in the form \(y = kx\), without any additional constant term on the right-hand side.
In our equation, we can see that there is an extra constant term, \(+4\), which means that the equation includes an additive constant that is not related to \(x\). Because of this, \(3x + 4\) does not fit the direct proportion form \(y = kx\).
However, if the constant term (\(+4\)) were not present, the equation would then be of the form \(y = 3x\), indicating a direct proportion where the constant of proportionality \(k\) is 3.
So the equation \(3x + 4 = y\) is not a direct proportion because it does not fit in the required form \(y = kx\).
Thus, the correct identification is:
No.
