To find the distance between two points $(-4, 6)$ and $(3, -7)$, we can use the distance formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Substituting the given points:

$d = \sqrt{(3 - (-4))^2 + (-7 - 6)^2}$

Simplifying:

$d = \sqrt{(3 + 4)^2 + (-7 - 6)^2}$ $d = \sqrt{(7)^2 + (-13)^2}$ $d = \sqrt{49 + 169}$ $d = \sqrt{218}$ $d \approx 14.8$

So, the distance between the points $(-4, 6)$ and $(3, -7)$ is approximately 14.8.

Do you want more details, or have any questions?

Here are 5 related questions to expand on this:

1. How does the distance formula relate to the Pythagorean theorem?
2. What is the distance between $(-2, 3)$ and $(5, -4)$?
3. What happens if the two points lie on a straight line, either horizontally or vertically?
4. Can you find the midpoint of $(-4, 6)$ and $(3, -7)$?
5. How would you calculate the distance if the points were in 3D space?

Tip: Always double-check your signs when applying the distance formula to avoid errors!