The given equation is:

$3y - 3x = 12$

To convert this into slope-intercept form $y = mx + b$, follow these steps:

1. Start by isolating the $y$-term on one side of the equation. Add $3x$ to both sides to get:

$3y = 3x + 12$

2. Now, divide everything by 3 to solve for $y$:

$y = x + 4$

So, the equation in slope-intercept form is:

$y = x + 4$

Where the slope $m = 1$ and the y-intercept $b = 4$.

Let me know if you need more details or have any questions! Here's some related math to explore:

1. How would the graph of $y = x + 4$ look?
2. What does the slope represent in a real-world context?
3. How can you find the slope and intercept for other linear equations?
4. What if the equation had a negative slope? How would that change the graph?
5. Can slope-intercept form be used to determine parallel or perpendicular lines?

Tip: Always isolate the variable $y$ first when converting to slope-intercept form!