To find the equation of the line passing through the points $(55, 6)$ and $(-5, -6)$, we can use the point-slope form of the equation of a line, which is:

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

where $m$ is the slope of the line, and $(x_1, y_1)$ is a point on the line.

Step 1: Calculate the Slope $m$

The slope $m$ is calculated using the formula:

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

Substitute the given points $(x_1, y_1) = (55, 6)$ and $(x_2, y_2) = (-5, -6)$:

$m = \frac{-6 - 6}{-5 - 55} = \frac{-12}{-60} = \frac{1}{5}$

Step 2: Use the Point-Slope Form

Using the point $(55, 6)$ and the slope $m = \frac{1}{5}$, the equation becomes:

$y - 6 = \frac{1}{5}(x - 55)$

Step 3: Simplify to Slope-Intercept Form (Optional)

We can simplify the equation to the slope-intercept form $y = mx + b$:

$y - 6 = \frac{1}{5}x - \frac{55}{5}$

$y = \frac{1}{5}x - 11 + 6$

$y = \frac{1}{5}x - 5$

Final Answer

The equation of the line is:

$y = \frac{1}{5}x - 5$

Would you like more details or have any questions?

Here are some related questions:

1. How do you convert a linear equation from point-slope form to standard form?
2. What is the significance of the slope in the equation of a line?
3. How do you find the equation of a line parallel to another line passing through a specific point?
4. Can you explain how to find the equation of a line perpendicular to a given line?
5. How do you find the midpoint between two points on a line?

Tip: When finding the equation of a line through two points, always calculate the slope first to ensure accuracy in your equation.