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The problem asks for the equation of a line in point-slope form, given the point \((-5, -7)\) and a slope of \(-\frac{1}{4}\).

The point-slope form of the equation of a line is:

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

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

Here, the slope \(m = -\frac{1}{4}\), and the point \((x_1, y_1)\) is \((-5, -7)\).

Substituting the values into the equation:

\[
y - (-7) = -\frac{1}{4}(x - (-5))
\]

Simplifying:

\[
y + 7 = -\frac{1}{4}(x + 5)
\]

Thus, the point-slope form of the equation is:

\[
y + 7 = -\frac{1}{4}(x + 5)
\]

This equation can be entered as:

\[
y - (-7) = -\frac{1}{4}(x - (-5))
\]

Let me know if you'd like further details or explanations.

Here are some follow-up questions you might find helpful:
1. How can this point-slope equation be converted to slope-intercept form?
2. How would you plot this line using the given equation?
3. What happens to the graph if the slope changes to a positive fraction?
4. Can you find the x- and y-intercepts of this line?
5. How would the equation change if the slope was 0?

**Tip:** The point-slope form is especially useful for quickly writing equations when a point and slope are known.

There is a line that includes the point (-5, -7) and has a slope of -1/4. What is its equation in point-slope form?

Find the equation of a line passing through the point (-5, -7) with a slope of -1/4 using point-slope form. This solution explains the key algebraic concepts and the point-slope formula, ideal for students in Grades 8-10.

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