To convert the equation \(2x - 6 + 3y = 0\) into the slope-intercept form \(y = mx + b\), follow these steps:

1. **Isolate the \(y\)-term**:  
   Start by moving the \(2x\) and \(-6\) terms to the other side of the equation by subtracting \(2x\) and adding \(6\) to both sides:
   \[
   3y = -2x + 6
   \]

2. **Solve for \(y\)**:  
   Divide the entire equation by \(3\) to isolate \(y\):
   \[
   y = \left(-\frac{2}{3}\right)x + 2
   \]

The equation is now in the slope-intercept form \(y = mx + b\), where:
- \(m = -\frac{2}{3}\) is the slope,
- \(b = 2\) is the y-intercept.

Would you like more details, or do you have any questions? 

Here are 5 related questions for further exploration:
1. How do you interpret the slope \(m\) in the context of a graph?
2. What does the y-intercept \(b = 2\) represent on the graph?
3. How would the graph of this equation change if the slope \(m\) were positive?
4. What are the x- and y-intercepts of this line?
5. How can you determine if two lines are parallel or perpendicular?

**Tip:** The slope \(m\) represents the rate of change of \(y\) with respect to \(x\), meaning for every unit increase in \(x\), \(y\) changes by \(m\) units.

Learn how to convert the equation 2x - 6 + 3y = 0 to the slope-intercept form y = mx + b with a detailed step-by-step solution. Understand the concepts of linear equations and slope-intercept form. Suitable for students in Grades 7-9.

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