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Is this a linear function?

3X + 9 = 25

(1 point)
Responses

yes
yes

no

1 answer

To determine if the equation \(3X + 9 = 25\) represents a linear function, we can rearrange it into the standard form of a linear equation.

  1. Start with the equation: \[ 3X + 9 = 25 \]

  2. Subtract 9 from both sides: \[ 3X = 16 \]

  3. Divide by 3: \[ X = \frac{16}{3} \]

This equation shows that \(X\) is isolated and doesn't depend on another variable (like \(Y\)), but it still represents a linear relationship. Moreover, in terms of function notation, we can express it in the form \(Y = mX + b\) by recognizing it as a constant function of \(X\). However, strictly speaking, the equation itself does not represent a function of two variables.

Since linear functions typically involve expressions that allow for both dependent and independent variables, this equation does not define a function in the traditional sense (where \(Y\) depends on \(X\)).

Thus, the answer is no, this is not a linear function in the sense of defining a relation between \(X\) and a dependent variable \(Y\).