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The problem asks to write the equation of a line in point-slope form. We are given:

- The point \( (8, -8) \)
- The slope \( m = \frac{5}{4} \)

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

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

Where:
- \( (x_1, y_1) \) is the given point, which in this case is \( (8, -8) \)
- \( m \) is the slope, \( \frac{5}{4} \)

Substitute these values into the formula:

\[
y - (-8) = \frac{5}{4}(x - 8)
\]

Simplifying the left-hand side:

\[
y + 8 = \frac{5}{4}(x - 8)
\]

This is the equation in point-slope form for the given line.

Would you like a detailed explanation of further steps, such as converting this to slope-intercept form or expanding it fully? 

Here are 5 related questions to expand your understanding:
1. How do you convert this equation into slope-intercept form?
2. What is the significance of the slope in the graph of the equation?
3. How do you find the x-intercept and y-intercept from this equation?
4. What changes in the equation if the slope is negative?
5. How would the equation change if the point was different but the slope stayed the same?

**Tip:** When working with the point-slope form, remember that you can easily convert it to slope-intercept form by solving for \( y \).

Una recta atraviesa el punto (8, -8) y tiene una pendiente igual a 5/4. Escribir una ecuación en la forma punto pendiente para esta recta.

Learn how to write the equation of a line passing through the point (8, -8) with a slope of 5/4 in point-slope form. This problem covers key algebraic concepts, including point-slope form and linear equations. Suitable for students in Grades 9-10.

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