To find the equation of the line that passes through the points $(-1, 6)$ and $(4, -4)$, we can use the slope-intercept form of a line:

$y = mx + b$

where $m$ is the slope, and $b$ is the y-intercept.

Step 1: Find the slope $m$

The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

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

Substitute the points $(-1, 6)$ and $(4, -4)$:

$m = \frac{-4 - 6}{4 - (-1)} = \frac{-4 - 6}{4 + 1} = \frac{-10}{5} = -2$

So, the slope of the line is $-2$.

Step 2: Use the slope-intercept form

Now that we have the slope $m = -2$, we can substitute it into the slope-intercept form $y = mx + b$. To find $b$, the y-intercept, we substitute one of the given points into the equation. Let's use the point $(-1, 6)$:

$6 = -2(-1) + b$

Simplifying:

$6 = 2 + b$

Solving for $b$:

$b = 6 - 2 = 4$

Step 3: Write the equation

Now that we have $m = -2$ and $b = 4$, the equation of the line is:

$y = -2x + 4$

This is the equation of the line that passes through the points $(-1, 6)$ and $(4, -4)$.

Would you like further details or have any questions? Here are 5 related questions:

1. How do you derive the slope formula from two points?
2. What is the point-slope form of a line equation?
3. Can you find the midpoint of the segment between $(-1, 6)$ and $(4, -4)$?
4. How do parallel lines relate in terms of slope?
5. What is the significance of the y-intercept in real-world problems?

Tip: Always verify your slope calculation as a first step, because it affects the entire equation.