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.