#### Answer

$y = -\frac{1}{3}x + 4$

#### Work Step by Step

We are given the points $(-6, 6)$ and the point $(3, 3)$.
Let's use the formula to find the slope $m$ given two points:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Let's plug in the values into this formula:
$m = \frac{3 - 6}{3 - (-6)}$
Subtract the numerator and denominator to simplify:
$m = \frac{-3}{9}$
To simplify, divide the numerator and denominator by their greatest common factor, $3$:
$m = -\frac{1}{3}$
Now that we have the slope, we can use one of the points and plug these values into the point-slope equation, which is given by the formula:
$y - y_1 = m(x - x_1)$
Let's plug in the points and slope into the formula:
$y - 3 = -\frac{1}{3}(x - 3)$
Use distribution to simplify:
$y - 3 = -\frac{1}{3}x - (-\frac{3}{3})$
Simplify the fraction by dividing by their greatest common factor, $3$:
$y - 3 = -\frac{1}{3}x + 1$
To change this equation into point-intercept form, we need to isolate $y$. To isolate $y$, we add $3$ to each side of the equation:
$y = -\frac{1}{3}x + 1 + 3$
Add constants to simplify:
$y = -\frac{1}{3}x + 4$
Now, we have the equation of the line in slope-intercept form.