To find the equation of a line with a given slope $m$ and passing through a specific point $(x_1, y_1)$, we use the point-slope form of the equation of a line:

$y - y_1 = m(x - x_1)$

Given:

• Slope $m = 0$
• Point $(-3, -9)$

Substitute the values into the point-slope form:

$y - (-9) = 0(x - (-3))$

Simplify the equation:

$y + 9 = 0 \times (x + 3)$

$y + 9 = 0$

Finally, subtract 9 from both sides to get the equation of the line:

$y = -9$

So, the equation of the line is:

$y = -9$

This is a horizontal line passing through $y = -9$.

Would you like any further details or have any questions?

Here are some related questions you might find helpful:

1. What is the general form of the equation of a horizontal line?
2. How do you find the equation of a vertical line passing through a given point?
3. What is the slope of a vertical line?
4. How do you find the distance between a point and a line?
5. What is the equation of a line perpendicular to a horizontal line?

Tip: A line with a slope of zero is always horizontal, and its equation is in the form $y = c$, where $c$ is the constant y-value.