Write an equation of the line that passes through the given points. (2,8) and (4,-4)

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.

Learn how to write the equation of a line passing through the points (2, 8) and (4, -4). This step-by-step solution covers slope calculation, point-slope form, and slope-intercept form. Suitable for students in Grades 8-10.

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