To find the equation of the line passing through the points $(9, -1)$ and $(-7, 4)$, we follow these steps:

1. Find the slope of the line (denoted by $m$):

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

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

Substituting the given points $(9, -1)$ and $(-7, 4)$:

$m = \frac{4 - (-1)}{-7 - 9} = \frac{4 + 1}{-7 - 9} = \frac{5}{-16} = -\frac{5}{16}$

2. Use the point-slope form of the equation of a line:

The point-slope form is given by:

$y - y_1 = m(x - x_1)$

Using the point $(9, -1)$ and the slope $m = -\frac{5}{16}$:

$y - (-1) = -\frac{5}{16}(x - 9)$

Simplifying the equation:

$y + 1 = -\frac{5}{16}(x - 9)$

This is the equation of the line in point-slope form.

Would you like more details on solving it further, or have any questions?

Here are 5 related questions:

1. How do you convert from point-slope form to slope-intercept form?
2. What happens when the line is vertical or horizontal?
3. How can you check if a point lies on a line?
4. How do you find the distance between two points?
5. How do you find the equation of a line parallel to a given line?

Tip: The slope of a vertical line is undefined, while a horizontal line has a slope of zero.