To write the equation [tex]\(6q = 3s - 9\)[/tex] in terms of the independent variable [tex]\(q\)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
6q = 3s - 9
\][/tex]
2. Isolate the term involving [tex]\(s\)[/tex] on one side of the equation. To do this, add 9 to both sides of the equation:
[tex]\[
6q + 9 = 3s
\][/tex]
3. Solve for [tex]\(s\)[/tex] by dividing both sides of the equation by 3:
[tex]\[
s = \frac{6q + 9}{3}
\][/tex]
4. Simplify the right side of the equation:
[tex]\[
s = \frac{6q}{3} + \frac{9}{3}
\][/tex]
[tex]\[
s = 2q + 3
\][/tex]
Therefore, the equation in terms of the independent variable [tex]\(q\)[/tex] is:
[tex]\[
f(q) = 2q + 3
\][/tex]
None of the other given options are correct. Thus, the correct function is:
[tex]\[
f(q) = 2q + 3
\][/tex]
