Write the equation of the line passing through the points left parenthesis 55 comma 6 right parenthesis and left parenthesis negative 5 comma negative 6 right parenthesis .

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.

Learn how to write the equation of a line passing through the points (55, 6) and (-5, -6) using the point-slope form of a line equation and the slope formula. This problem involves calculating the slope, using it to derive the equation of the line, and simplifying it to slope-intercept form. Suitable for students in Grades 7-9.

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