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To find the equation of a line in point-slope form, we use the formula:

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

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

Given:
- Slope \(m = -7\)
- Point \((x_1, y_1) = (-5, -8)\)

Substituting the values into the point-slope formula:

\[
y - (-8) = -7(x - (-5))
\]

Simplifying:

\[
y + 8 = -7(x + 5)
\]

So, the equation of the line in point-slope form is:

\[
y + 8 = -7(x + 5)
\]

Would you like any further details on this solution? 

Here are 5 related questions to extend this topic:
1. How can you convert this point-slope form into slope-intercept form?
2. What is the significance of point-slope form in geometry?
3. How can you find the y-intercept from the given line equation?
4. What would the equation be if the slope were positive instead of negative?
5. How do you determine the slope between two points?

**Tip**: In point-slope form, the point \((x_1, y_1)\) on the line is directly substituted into the equation, allowing quick identification of specific lines.

A line with a slope of -7 passes through the point (-5, -8). What is its equation in point-slope form?

Find the equation of a line with a slope of -7 passing through the point (-5, -8) using the point-slope formula. This problem focuses on key linear equation concepts suitable for Grades 8-10.

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