Consider the function represented by the equation y-6x-9=0. Which answer shows the equation written in function notation with x

Question

2 months ago

12

as the independent variable? A.f(x)= 6x+9 B. f(x)=1/6x+3/2 C. f(y)=1/6y+3/2

2 answers:

AnnZ [12.3K] · Answer 1 · 2026-02-21T04:08:11+03:00

6 0

we possess

$y-6x-9=0$

Step $1$

Eliminate the variable y

$y-6x-9=0$

Add $(6x+9)$ to each side

$y-6x-9+(6x+9)=0+(6x+9)$

$y=(6x+9)$

Step $2$

Change to function notation

Define

$f(x)=y$

$f(x)=(6x+9)$

thus

the result is

$f(x)=(6x+9)$

AnnZ [12.3K] · Answer 2 · 2026-02-21T04:09:39+03:00

Solution:

When an equation of a function is expressed, there are two types of variables

1. Independent variable

2. Dependent Variable

A variable is classified as independent if it can assume fixed values freely.

Conversely, a variable is termed dependent if it relies on another variable within the equation.

The equation in question is y - 6x - 9 = 0

As we need to formulate a function where x is the independent variable and y acts as the dependent variable.

This transforms the linear equation to

y = 6x + 9

f(x) = 6x + 9 →→Option (A)

This correctly depicts a function where x is independent and y is dependent, as varying values of x yield different values of y.