To find the equation of a line passing through two points, we use the slope-intercept form of a line:

$y = mx + b$

Step 1: Find the slope ($m$)

The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the points $(1, -6)$ and $(-6, -6)$:

$m = \frac{-6 - (-6)}{-6 - 1} = \frac{0}{-7} = 0$

Thus, the slope of the line is $m = 0$.

Step 2: Write the equation

Since the slope is $0$, the line is horizontal. A horizontal line has a constant $y$-value equal to the $y$-coordinate of any point on the line. Both points have $y = -6$. Therefore, the equation of the line is:

$y = -6$

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This is the final equation of the line.

Would you like a more detailed explanation or examples of horizontal lines? Here are some related questions:

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1. What is the slope of a vertical line passing through two points with the same $x$-coordinate?
2. Can a horizontal line have a different $y$-coordinate for any two points on it?
3. How would the equation change if the line were vertical instead of horizontal?
4. What is the geometric interpretation of a slope of zero?
5. How do we determine the $x$-intercept for a horizontal line?

Tip: Horizontal lines always have equations of the form $y = c$, where $c$ is a constant, while vertical lines have equations of the form $x = c$.