To convert the equation $3y - 3x = 9$ into the slope-intercept form, $y = mx + b$, follow these steps:

1. Isolate the $y$ term: Start by adding $3x$ to both sides of the equation: $3y = 3x + 9$

2. Solve for $y$ by dividing every term by 3: $y = \frac{3x}{3} + \frac{9}{3}$ Simplifying the fractions gives: $y = x + 3$

So, the equation in slope-intercept form is $y = x + 3$, where:

• The slope $m = 1$,
• The y-intercept $b = 3$.

Would you like any further details or explanations?

Here are 5 related questions to further your understanding:

1. What is the slope and y-intercept of the equation $y = 2x - 5$?
2. How would you convert the equation $2y - 4x = 8$ into slope-intercept form?
3. What is the significance of the slope in the equation $y = mx + b$?
4. How can you graph the equation $y = x + 3$ on the coordinate plane?
5. How does changing the value of $b$ in the equation $y = mx + b$ affect the graph?

Tip: When converting an equation to the slope-intercept form, always focus on isolating $y$ to easily identify the slope and y-intercept.