To rewrite the equation [tex]\(y - 6x - 9 = 0\)[/tex] in function notation with [tex]\(x\)[/tex] as the independent variable, we need to express [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex].
1. Start with the given equation:
[tex]\[
y - 6x - 9 = 0
\][/tex]
2. Move the term involving [tex]\(x\)[/tex] and the constant to the other side of the equation by adding [tex]\(6x\)[/tex] and [tex]\(9\)[/tex] to both sides:
[tex]\[
y = 6x + 9
\][/tex]
3. The equation [tex]\(y = 6x + 9\)[/tex] expresses [tex]\(y\)[/tex] as a function of [tex]\(x\)[/tex].
4. In function notation, this is typically written as:
[tex]\[
f(x) = 6x + 9
\][/tex]
5. Reviewing the provided options, the equation written in function notation, with [tex]\(x\)[/tex] as the independent variable, is:
[tex]\[
f(x) = 6x + 9
\][/tex]
Therefore, the correct answer is:
[tex]\[ f(x) = 6x + 9 \][/tex]
