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.