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Let's walk through how to solve the problem using the **point-slope form of a line equation**.

The general point-slope form is:

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

where:
- \( (x_1, y_1) \) is a point on the line
- \( m \) is the slope of the line

### Step 1: Find the slope \( m \)
The slope \( m \) between two points \( (x_1, y_1) = (-8, -8) \) and \( (x_2, y_2) = (-7, 9) \) is calculated using the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - (-8)}{-7 - (-8)}
\]

Simplify:

\[
m = \frac{9 + 8}{-7 + 8} = \frac{17}{1} = 17
\]

### Step 2: Write the equation in point-slope form
Using the point \( (-7, 9) \) (though either point will work), we substitute \( m = 17 \), \( x_1 = -7 \), and \( y_1 = 9 \) into the point-slope formula:

\[
y - 9 = 17 (x + 7)
\]

This is the point-slope equation for the line passing through the two given points.

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Do you need further steps, such as simplifying or transforming this equation into another form (like slope-intercept)? 

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Here are **5 related questions**:
1. How do you convert a point-slope equation into slope-intercept form?
2. What would the equation look like if you used the point \( (-8, -8) \)?
3. How do you determine if two lines are parallel or perpendicular based on their slopes?
4. What is the significance of the slope value in real-world contexts?
5. How do you find the x- and y-intercepts from a point-slope equation?

**Tip:** Always double-check arithmetic when calculating slope, as sign errors are common mistakes!

Complete the point-slope equation of the line through (-8, -8) and (-7, 9).

Learn how to write the point-slope equation of a line through the points (-8, -8) and (-7, 9) with a detailed step-by-step solution. This problem covers key algebraic concepts, including calculating the slope and applying the point-slope form. Suitable for students in Grades 8-10.

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