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The problem asks to write a point-slope equation for a line with a slope of \(-\frac{8}{7}\), passing through the point \((4, 4)\).

The point-slope form of a line's equation 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.

Given:
- Slope \(m = -\frac{8}{7}\),
- Point \((x_1, y_1) = (4, 4)\).

Substitute these values into the point-slope formula:

\[
y - 4 = -\frac{8}{7}(x - 4)
\]

This matches option **C** in the multiple-choice answers. 

Would you like a deeper explanation or have any questions about this? 

Here are 5 related questions to help further your understanding:
1. How would the equation change if the slope were positive?
2. What is the slope-intercept form of this same line equation?
3. How do you convert from point-slope form to standard form?
4. How do you find the slope if only given two points?
5. What happens to the equation if the point used is \((0, 0)\)?

**Tip:** The point-slope form is especially useful when you know a specific point on the line and its slope, making it straightforward to write the equation quickly!

The slope of the line is -8/7. Write a point-slope equation of the line using the coordinates of the labeled point (4, 4).

Learn how to write a point-slope equation for a line with a slope of -8/7 that passes through the point (4, 4). This problem covers key concepts in algebra, including linear equations and the point-slope form. Suitable for students in Grades 8-10.

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