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We are tasked with finding the equation of a line in point-slope form. The given information includes the slope \( \frac{1}{7} \) and the point \( (-10, -6) \).

The point-slope form of a line is given by:

\[
y - y_1 = m(x - x_1)
\]

Where:
- \( m \) is the slope,
- \( (x_1, y_1) \) is the point on the line.

Using the given values:
- \( m = \frac{1}{7} \),
- \( x_1 = -10 \),
- \( y_1 = -6 \),

We substitute these into the point-slope formula:

\[
y - (-6) = \frac{1}{7}(x - (-10))
\]

Simplifying both sides:

\[
y + 6 = \frac{1}{7}(x + 10)
\]

Thus, the equation in point-slope form is:

\[
y + 6 = \frac{1}{7}(x + 10)
\]

Would you like a more detailed explanation or have any further questions?

Here are 5 related questions to expand your understanding:
1. How would you convert this equation into slope-intercept form?
2. What is the equation of the line with a slope of \( -\frac{2}{5} \) passing through the point \( (3, -7) \)?
3. How do you find the slope of a line given two points?
4. What is the general form of the equation of a line, and how does it differ from point-slope form?
5. How can you verify if a point lies on a given line?

**Tip:** Always check your equation by substituting the given point back into it to ensure it's correct.

A line with a slope of \( \frac{1}{7} \) passes through the point \((-10, -6)\). What is its equation in point-slope form?

Learn how to find the equation of a line with a slope of 1/7 that passes through the point (-10, -6) using the point-slope formula. This problem involves applying the point-slope form equation y - y1 = m(x - x1) for linear equations in coordinate geometry.

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