To solve the equation \( 9x - 6 = -8 \), we can first rearrange the equation into the form \( 9x = -8 + 6 \), which simplifies to \( 9x = -2 \). From this, we can find \( x \) by dividing both sides by 9:
\[ x = -\frac{2}{9} \]
To graph a function that will help us solve this equation, we can set \( f(x) = 9x - 6 \) and look for the \( x \)-value where this function equals \(-8\).
So we can represent the equation as:
- \( f(x) = 9x - 6 \)
- \( g(x) = -8 \) (a horizontal line)
We need to find the intersection point of \( f(x) \) and \( g(x) \).
Now let's analyze the options given to decide which one represents the line \( g(x) = -8 \):
- \( F(x) = 9x + 2 \) (not correct)
- \( f(x) = 9x - 14 \) (not correct)
- \( f(x) = 17x - 6 \) (not correct)
- \( f(x) = -6 \) (not correct)
Since none of these options represent \( g(x) = -8 \), we could conclude that none of the options provided would graphically solve the equation.
However, the correct representation would have been a horizontal line \( g(x) = -8 \) and the function \( f(x) = 9x - 6 \). If we had to pick any of the options related to the original equation, it is worth noting only the \( f(x) = 9x - 6 \) function can be evolved towards solving the intersection since it comes directly from the rearranged equation itself.
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