Let's find the equation of the line that passes through the points \((3, -2)\) and \((-1, 6)\).

### Step 1: Calculate the slope \( m \)
The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the given points \((3, -2)\) and \((-1, 6)\):
\[
m = \frac{6 - (-2)}{-1 - 3} = \frac{6 + 2}{-4} = \frac{8}{-4} = -2
\]

### Step 2: Use the slope-intercept form \( y = mx + b \)
We have the slope \( m = -2 \). Now, let's use one of the points to find the y-intercept \( b \). We can use the point \((3, -2)\):

\[
y = mx + b
\]
\[
-2 = -2(3) + b
\]
\[
-2 = -6 + b
\]
\[
b = -2 + 6 = 4
\]

### Final Equation
Thus, the equation of the line is:
\[
y = -2x + 4
\]

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. What is the distance between the points \((3, -2)\) and \((-1, 6)\)?
2. How would the equation change if the slope were positive instead?
3. How can you find the equation using the point-slope form?
4. What is the significance of the y-intercept in this equation?
5. Can you determine the x-intercept of this line?

**Tip:** Always simplify your slope and intercept calculations fully to avoid mistakes in the final equation.

Learn how to find the equation of a line passing through the points (3, -2) and (-1, 6) with detailed step-by-step calculations. This problem covers key concepts in analytic geometry, including the slope formula and slope-intercept form. Suitable for students in Grades 7-9.

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