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!