Question

What function should be graphed in order to solve the equation 9x - 6= -8
A)f(x)=17x-6
B)f(x)=9x-14
C)f(x)=9x+2
D)x-6

Answer 1

To solve the equation \( 9x - 6 = -8 \), we can first isolate \( x \) by rearranging the equation:

1. Add 6 to both sides:
\[
9x = -8 + 6
\]
\[
9x = -2
\]

2. Now, divide by 9:
\[
x = -\frac{2}{9}
\]

Next, we want to determine which of the given functions will result in solving the equation \( 9x - 6 = -8 \) in the form of \( f(x) = 0 \).

Rearranging the original equation gives us:
\[
9x - 6 + 8 = 0 \quad \text{or} \quad 9x + 2 = 0
\]
This means we want to graph the function \( f(x) = 9x + 2 \) and find where it crosses the x-axis (i.e., where \( f(x) = 0 \)).

Looking at the options provided:
- A) \( f(x) = 17x - 6 \)
- B) \( f(x) = 9x - 14 \)
- C) \( f(x) = 9x + 2 \)
- D) \( f(x) = x - 6 \)

The correct function to graph for solving the equation is:
**C) \( f(x) = 9x + 2 \)**.