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 identify which equation correctly represents the given equation [tex]\( y - 6x - 9 = 0 \)[/tex] in function notation with [tex]\( x \)[/tex] as the independent variable, let's go through the steps to rewrite the equation.

1. Start with the original equation:
[tex]\[ y - 6x - 9 = 0 \][/tex]

2. Solve for [tex]\( y \)[/tex]:
[tex]\[ y = 6x + 9 \][/tex]

3. In function notation, we express [tex]\( y \)[/tex] as [tex]\( f(x) \)[/tex] because [tex]\( y \)[/tex] is dependent on the independent variable [tex]\( x \)[/tex]:
[tex]\[ f(x) = 6x + 9 \][/tex]

Given the options:
- [tex]\( f(x) = 6x + 9 \)[/tex]
- [tex]\( f(x) = \frac{1}{6}x + \frac{3}{2} \)[/tex]
- [tex]\( f(y) = 6y + 9 \)[/tex]
- [tex]\( f(y) = \frac{1}{6}y + \frac{3}{2} \)[/tex]

The correct equation written in function notation with [tex]\( x \)[/tex] as the independent variable is:
[tex]\[ f(x) = 6x + 9 \][/tex]

So, the first option [tex]\( f(x) = 6x + 9 \)[/tex] is correct. Therefore, the answer to the question is:

[tex]\[ 1 \][/tex]