The problem asks for the equation of the line in slope-intercept form that passes through the points $(0, 3)$ and $(3, -6)$. Let's solve step by step:

Step 1: Find the slope ($m$):

The slope formula is:

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

Substitute $(x_1, y_1) = (0, 3)$ and $(x_2, y_2) = (3, -6)$:

$m = \frac{-6 - 3}{3 - 0} = \frac{-9}{3} = -3$

Step 2: Write the slope-intercept form ($y = mx + b$):

Now we know the slope is $m = -3$. Using the point $(0, 3)$, substitute into the equation to find $b$ (the y-intercept):

$y = mx + b \implies 3 = -3(0) + b \implies b = 3$

Thus, the equation of the line is:

$y = -3x + 3$

Step 3: Match the answer:

The correct option is:

$\boxed{y = -3x + 3}$

Let me know if you'd like further clarification or details!

Here are 5 related questions for you to explore:

1. How would you find the equation of a line if you are given its slope and one point?
2. What happens to the slope of a line if the two points are flipped in order?
3. How can you verify that a point lies on a given line?
4. What is the significance of the y-intercept in real-life scenarios?
5. Can two different lines have the same slope and different y-intercepts? Why?

Tip: Always double-check your slope and intercept calculations by substituting one of the given points into your equation.