To find the equation of the line that is perpendicular to the given line and passes through a specific point, we can follow these steps:

1. Find the Slope of the Given Line

The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

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

For the given points $(-4, -3)$ and $(4, 1)$:

$m = \frac{1 - (-3)}{4 - (-4)} = \frac{1 + 3}{4 + 4} = \frac{4}{8} = \frac{1}{2}$

So, the slope of the given line is $m = \frac{1}{2}$.

2. Find the Slope of the Perpendicular Line

The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. Therefore, the slope $m'$ of the perpendicular line is:

$m' = -\frac{1}{m} = -\frac{1}{\frac{1}{2}} = -2$

3. Write the Equation in Point-Slope Form

The point-slope form of a line's equation is:

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

You mentioned the point the perpendicular line passes through as $(x_1, 3)$. However, it seems like the x-coordinate was not provided. If we assume the point to be $(x_1, 3)$, the equation in point-slope form would be:

$y - 3 = -2(x - x_1)$

Conclusion

The equation of the line perpendicular to the given line and passing through the point $(x_1, 3)$ in point-slope form is:

$\boxed{y - 3 = -2(x - x_1)}$

If you provide the x-coordinate for the point, I can give you the exact equation.

Would you like more details on this process, or do you have any questions? Here are some related questions:

1. How do you find the equation of a line given two points?
2. What is the relationship between the slopes of parallel and perpendicular lines?
3. How can you convert from point-slope form to slope-intercept form?
4. How do you determine the slope of a line from its equation?
5. What is the general formula for the distance between two points on a coordinate plane?

Tip: Always remember, for perpendicular lines, the product of their slopes equals $-1$.