Given that the slope of the line is 0, this indicates that the line is horizontal. For any horizontal line, the equation of the line is in the form:

$y = c$

where $c$ is the y-coordinate of any point on the line.

Given the point $(- \frac{8}{9}, - \frac{8}{7})$, the y-coordinate is $- \frac{8}{7}$. Therefore, the equation of the line is:

$y = - \frac{8}{7}$

This is the simplified equation of the line.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:

1. How do you find the slope of a line given two points?
2. What is the general form of a linear equation?
3. How do you identify if a line is vertical or horizontal?
4. What does a slope of zero mean geometrically?
5. How can you determine the equation of a line parallel to a given line?

Tip: Remember that the equation of a horizontal line is always $y = \text{constant}$, where the constant is the y-coordinate of any point on the line.