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

Step 1: Find the slope $m$

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

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

Substitute the given points $(-1, 4)$ and $(3, -4)$ into the formula:

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

Step 2: Use the point-slope form equation

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

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

We can use either of the given points. Let's use $(-1, 4)$:

$y - 4 = -2(x - (-1)) = -2(x + 1)$

Step 3: Simplify (optional)

We could leave it as is, or distribute to simplify:

$y - 4 = -2x - 2$ $y = -2x + 2$

So, the equation in point-slope form is:

$y - 4 = -2(x + 1)$

Do you want more details or have any questions about this?

---

Here are 5 related questions you can try:

1. How do you convert the point-slope form to slope-intercept form?
2. What is the general form of the equation of a line?
3. How do you find the equation of a line if you're given the slope and one point?
4. What happens to the point-slope form if the slope is zero?
5. How can you find the midpoint between two points?

Tip: Point-slope form is very useful when you know the slope and one point on the line!