To find the equation of the line passing through the points $(-2, 8)$ and $(4, -4)$, we use the point-slope form of the equation of a line:

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

Step 1: Calculate the slope ($m$):

The slope is given by:

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

Substitute the coordinates of the points: $m = \frac{-4 - 8}{4 - (-2)} = \frac{-12}{6} = -2$

Step 2: Use the slope and one point to find the equation:

Using the point $(-2, 8)$ and $m = -2$, substitute into the point-slope form:

$y - 8 = -2(x - (-2))$

Simplify: $y - 8 = -2(x + 2)$

$y - 8 = -2x - 4$

$y = -2x + 4$

Final Answer:

The equation of the line is: $y = -2x + 4$

Would you like me to explain further or verify with a different point?

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Relative Questions:

1. How do you determine the slope of a line from two points?
2. What is the general form of a linear equation, and how does it differ from the slope-intercept form?
3. How would the equation change if one of the points were different?
4. Can you verify if both points satisfy the equation $y = -2x + 4$?
5. How can we rewrite this line equation in standard form?

Tip:

When finding the equation of a line, always double-check your slope calculation to ensure accuracy!