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

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

where $m$ is the slope of the line, and $(x_1, y_1)$ is one of the points on the line.

Step 1: Find the Slope ($m$)

The slope $m$ is calculated as:

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

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

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

Step 2: Use the Point-Slope Form

Now, substitute $m = -2$ and one of the points, say $(1, -4)$, into the point-slope form:

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

Simplify the equation:

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

Step 3: Simplify to the Slope-Intercept Form ($y = mx + b$)

Expand and simplify:

$y + 4 = -2x + 2$

Subtract 4 from both sides:

$y = -2x - 2$

So, the equation of the line in terms of $x$ is:

$\boxed{y = -2x - 2}$

Would you like more details or have any questions?

Here are some related questions to explore:

1. How would you find the equation of a line given its slope and one point?
2. What is the general form of the equation of a line?
3. How do you determine if two lines are parallel or perpendicular?
4. Can you find the y-intercept of a line given two points?
5. How does changing the slope affect the steepness of a line?

Tip: When calculating the slope between two points, remember that a negative slope means the line is decreasing (going downwards) as it moves from left to right.