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The problem asks for the equation of a line that passes through the point \((4, -1)\) and has a slope of \(-\frac{5}{4}\).

We can use the **point-slope form** of the equation of a line:

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

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

Given:
- Slope \(m = -\frac{5}{4}\),
- Point \((x_1, y_1) = (4, -1)\),

Substitute these into the point-slope form:

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

Simplifying:

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

Now, distribute the slope:

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

Subtract 1 from both sides:

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

Thus, the equation of the line is:

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

Would you like any further details or explanation?

Here are 5 related questions for deeper understanding:
1. How do you convert a point-slope equation into slope-intercept form?
2. What is the slope of a line perpendicular to this one?
3. How would the equation change if the slope were positive?
4. What would be the equation if the line passed through a different point, say \((2, 3)\)?
5. How can you graph this line on a coordinate plane?

**Tip:** Always check the signs of your slope and y-intercept carefully when working with line equations to avoid simple mistakes!

What is the equation of the line that passes through the point (4, -1) and has a slope of -5/4?

Learn how to find the equation of a line passing through the point (4, -1) with a slope of -5/4 using the point-slope formula. This algebra problem is suitable for students in Grades 8-10 and covers key concepts like slope-intercept form and linear equations.

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