To find the slope-intercept form of the equation of a line, we follow these steps:

1. Find the slope (m):

The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Using the points $(4, -1)$ and $(0, 0)$:

$m = \frac{0 - (-1)}{0 - 4} = \frac{1}{-4} = -\frac{1}{4}$

2. Use the slope-intercept form:

The slope-intercept form of a line is:

$y = mx + b$

We know the slope $m = -\frac{1}{4}$ and that the line passes through the point $(0, 0)$, which is the y-intercept, so $b = 0$.

3. Write the equation:

Now that we have the slope and intercept, the equation of the line is:

$y = -\frac{1}{4}x$

This is the slope-intercept form of the equation of the line passing through the points $(4, -1)$ and $(0, 0)$.

Would you like more details on this process, or have any questions?

Here are some related questions to expand your understanding:

1. What would be the equation of the line if the points were different, such as $(2, 3)$ and $(6, 1)$?
2. How do you find the equation of a line given its slope and a point?
3. What is the significance of the slope in the graph of a line?
4. How would the equation change if the line had a different y-intercept?
5. How do you convert between slope-intercept form and standard form?

Tip: A slope of $-\frac{1}{4}$ means for every 4 units you move horizontally to the right, the line drops 1 unit vertically.