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The problem asks us to use the point-slope form to write the equation of a line that passes through the point \((8, -17)\) with a slope of \(-\frac{1}{4}\).

### Point-slope form of a line:
The point-slope form of a line is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope.

### Applying the values:
Here, the point is \( (x_1, y_1) = (8, -17) \) and the slope \( m = -\frac{1}{4} \).

Substituting into the point-slope form:
\[
y - (-17) = -\frac{1}{4}(x - 8)
\]
This simplifies to:
\[
y + 17 = -\frac{1}{4}(x - 8)
\]

This is the equation in point-slope form. If you'd like, we can convert this into slope-intercept form or simplify further.

Do you need any additional explanations? 

Here are 5 questions that could help deepen your understanding:
1. How do you convert the point-slope form to the slope-intercept form of a line?
2. What are the advantages of using point-slope form over other forms like slope-intercept?
3. Can you find the y-intercept of this line based on the current equation?
4. How do you graph a line using the point-slope form?
5. How would the equation change if the slope were positive instead of negative?

**Tip**: Remember that point-slope form is very useful when you have one point and the slope, making it easy to write the equation without converting to other forms.

Use point-slope form to write the equation of a line that passes through the point (8, -17) with slope -1/4.

Learn how to use the point-slope form to write the equation of a line passing through (8, -17) with a slope of -1/4. This algebra problem is ideal for students in Grades 8-10, covering linear equations and their applications.

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