To rewrite the equation [tex]\(\frac{1}{16} x + \frac{1}{320} y - 29 = 0\)[/tex] as a function of [tex]\(x\)[/tex], follow these steps:
1. Isolate the term containing [tex]\(y\)[/tex]: First, let's isolate [tex]\(\frac{1}{320} y\)[/tex] by moving the other terms to the right side of the equation.
[tex]\[
\frac{1}{320} y = -\frac{1}{16} x + 29
\][/tex]
2. Eliminate the fraction involving [tex]\(y\)[/tex]: To eliminate the fraction [tex]\(\frac{1}{320}\)[/tex], multiply both sides of the equation by 320.
[tex]\[
y = 320 \left( -\frac{1}{16} x + 29 \right)
\][/tex]
3. Distribute the constant 320 to both terms inside the parentheses:
[tex]\[
y = 320 \cdot -\frac{1}{16} x + 320 \cdot 29
\][/tex]
4. Simplify the terms:
[tex]\[
y = -20x + 9280
\][/tex]
5. Rewrite as a function of [tex]\(x\)[/tex]: Let's express [tex]\(y\)[/tex] as [tex]\(f(x)\)[/tex].
[tex]\[
f(x) = -20x + 9280
\][/tex]
Now we compare our result to the given options:
A. [tex]\(f(x) = -9,280 + \frac{1}{16} x\)[/tex]
B. [tex]\(f(x) = 9,280 - 20 x \)[/tex]
C. [tex]\(f(x) = -9,280 + 20 x\)[/tex]
D. [tex]\(f(x) = 9,280 - \frac{1}{16} x\)[/tex]
The correct option that matches our result, [tex]\(f(x) = -20x + 9280\)[/tex], is:
B. [tex]\(f(x) = 9,280 - 20 x\)[/tex]
