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Does the equation below represent a direct proportion?

[tex]3x + 4 = y[/tex]

If yes, identify the constant of proportionality.

A. Yes, [tex]x[/tex]
B. No
C. Yes, 4
D. Yes, 3

Sagot :

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.