To write the equation of the line passing through the points $(2, 8)$ and $(4, -4)$, we follow these steps:

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Step 1: Find the slope ($m$)

The slope of a line is given by the formula:

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

Substitute the coordinates $(x_1, y_1) = (2, 8)$ and $(x_2, y_2) = (4, -4)$:

$m = \frac{-4 - 8}{4 - 2} = \frac{-12}{2} = -6$

So, the slope is $m = -6$.

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Step 2: Use the point-slope form of the equation

The point-slope form is:

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

Using the slope $m = -6$ and the point $(2, 8)$:

$y - 8 = -6(x - 2)$

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Step 3: Simplify to slope-intercept form ($y = mx + b$)

Distribute and simplify:

$y - 8 = -6x + 12$

$y = -6x + 12 + 8$

$y = -6x + 20$

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Final Answer:

The equation of the line is:

$y = -6x + 20$

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Let me know if you'd like to see further details or have any questions! 😊

Here are 5 related questions to explore:

1. How do you find the equation of a line given a slope and a point?
2. What does the slope represent geometrically on a graph?
3. How would the equation change if the points were swapped?
4. How do you write the equation of a line in standard form?
5. How can you verify that a point lies on a given line?

Tip: When finding the equation of a line, using the point-slope form first ensures accuracy, especially with fractions or negatives.