Question

Is this a linear function?

3X + 9 = 25

(1 point)
Responses

yes
yes

no

Answer 1

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 \(Y\).