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.

Learn how to convert the equation 3y - 3x = 9 to the slope-intercept form y = mx + b with a step-by-step solution. This problem covers linear equations and the slope-intercept form concept, suitable for students in Grades 7-9.

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