To rewrite the given equation [tex]\(680x + 10y - 1000 = 0\)[/tex] as a function of [tex]\(x\)[/tex], we need to isolate [tex]\(y\)[/tex] on one side of the equation. Here are the detailed steps:
1. Start with the given equation:
[tex]\[
680x + 10y - 1000 = 0
\][/tex]
2. Move [tex]\(680x\)[/tex] and [tex]\(-1000\)[/tex] to the right side of the equation by adding [tex]\(-680x\)[/tex] and [tex]\(1000\)[/tex] to both sides:
[tex]\[
10y = -680x + 1000
\][/tex]
3. Solve for [tex]\(y\)[/tex] by dividing every term by 10:
[tex]\[
y = \frac{-680x + 1000}{10}
\][/tex]
4. Simplify the fractions:
[tex]\[
y = -68x + 100
\][/tex]
So, we can express [tex]\(y\)[/tex] as a function of [tex]\(x\)[/tex]:
[tex]\[
f(x) = 100 - 68x
\][/tex]
Therefore, the correct answer is:
C. [tex]\(f(x) = 100 - 68x\)[/tex]
