To find the equation of the line that passes through the points $(3, 6)$ and $(1, -2)$, we can use the point-slope form of the line equation:

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

First, we need to calculate the slope $m$ of the line using the formula:

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

Substituting the given points $(x_1, y_1) = (3, 6)$ and $(x_2, y_2) = (1, -2)$:

$m = \frac{-2 - 6}{1 - 3} = \frac{-8}{-2} = 4$

Now that we have the slope $m = 4$, we can use the point-slope form with the point $(3, 6)$:

$y - 6 = 4(x - 3)$

Expanding and simplifying to get the equation in slope-intercept form $y = mx + b$:

$y - 6 = 4x - 12$ $y = 4x - 6$

So, the equation of the line is:

$\boxed{y = 4x - 6}$

Would you like more details or have any questions?

Relative Questions:

1. How do you find the slope of a line given two points?
2. What is the difference between point-slope form and slope-intercept form of a line?
3. How do you convert from point-slope form to slope-intercept form?
4. Can you find the equation of a line parallel to $y = 4x - 6$ passing through another point?
5. What is the significance of the y-intercept in the equation $y = 4x - 6$?

Tip:

Always double-check your calculations when finding the slope to ensure the correct sign and value, as it directly affects the line equation.