Consider the function represented by the equation [tex]y - 6x - 9 = 0[/tex]. Which answer shows the equation written in function notation with [tex]x[/tex] as the independent variable?

A. [tex]f(x) = 6x + 9[/tex]

B. [tex]f(x) = \frac{1}{6}x + \frac{3}{2}[/tex]

C. [tex]f(y) = 6y + 9[/tex]

D. [tex]f(y) = \frac{1}{6}y + \frac{3}{2}[/tex]



Answer :

To convert a given equation into function notation with \( x \) as the independent variable, follow these steps:

1. Given equation: \( y - 6x - 9 = 0 \).

2. Isolate \( y \) in terms of \( x \):
[tex]\[ y = 6x + 9 \][/tex]

3. Rewrite this equation in function notation:
The variable \( y \) on the left-hand side is conventionally replaced with \( f(x) \) to indicate that \( y \) is a function of \( x \). Thus,
[tex]\[ f(x) = 6x + 9 \][/tex]

4. Compare with the given options to find the correct answer:
- Option 1: \( f(x) = 6x + 9 \)
- Option 2: \( f(x) = \frac{1}{6}x + \frac{3}{2} \)
- Option 3: \( f(y) = 6y + 9 \)
- Option 4: \( f(y) = \frac{1}{6}y + \frac{3}{2} \)

From our steps, we see that the equation \( f(x) = 6x + 9 \) matches Option 1.

Therefore, the correct answer is:
[tex]\[ f(x) = 6x + 9 \][/tex]

Hence, the correct option is:
[tex]\[ 1 \][/tex]