Question

what function should be graphed in order to solve the equation 9x - 6 = -8

Answer 1

To solve the equation \( 9x - 6 = -8 \) graphically, you can rearrange it into a standard form that can easily be graphed. Here’s how you can do it:

1. **Rearrange the equation**: First, isolate \( x \) on one side of the equation.

\[
9x - 6 = -8 \implies 9x = -8 + 6 \implies 9x = -2 \implies x = -\frac{2}{9}
\]

2. **Graph the functions**: To solve it graphically, you can graph two functions:
- \( y = 9x - 6 \)
- \( y = -8 \)

3. **Plot the graphs**:
- For \( y = 9x - 6 \), this is a straight line with a slope of \( 9 \) and a y-intercept of \( -6 \).
- For \( y = -8 \), this is a horizontal line where the y-value is always \(-8\).

4. **Find the intersection**: The solution to the equation \( 9x - 6 = -8 \) corresponds to the \( x \)-coordinate of the intersection point of these two lines.

By plotting these two functions, the \( x \)-coordinate of their intersection will give you the value of \( x \) that satisfies the original equation. In this case, you would find \( x = -\frac{2}{9} \).