To find the slope-intercept form of the equation \(3x - 2y = 6\), we need to rearrange it into the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

### Steps:

1. Start with the given equation:
   \[
   3x - 2y = 6
   \]

2. Isolate the \(y\)-term on one side. Subtract \(3x\) from both sides:
   \[
   -2y = -3x + 6
   \]

3. Solve for \(y\) by dividing both sides of the equation by \(-2\):
   \[
   y = \frac{-3x + 6}{-2}
   \]

4. Simplify the fractions:
   \[
   y = \frac{-3}{-2}x + \frac{6}{-2}
   \]
   \[
   y = \frac{3}{2}x - 3
   \]

### Final equation:
The slope-intercept form is:
\[
y = \frac{3}{2}x - 3
\]
Here, the slope \(m = \frac{3}{2}\) and the y-intercept \(b = -3\).

Would you like further details or have any questions?

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Here are 5 related questions to explore further:
1. How can we find the slope given two points on a line?
2. What is the equation of a line that is parallel to this one?
3. How can you calculate the x-intercept of this line?
4. How do we convert from slope-intercept form to standard form?
5. How would the graph of this equation look?

**Tip**: The slope \(m\) represents the steepness of a line: a positive slope means the line rises as you move from left to right.

3x - 2y = 6 find the slope-intercept form

Learn how to convert the linear equation 3x - 2y = 6 into slope-intercept form with this step-by-step guide. This problem covers key algebra concepts, including isolating variables and simplifying expressions. Perfect for students in Grades 8-10.

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