The problem requires us to convert the equation $3x - 2y = -6$ into slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Then, we need to identify the slope $m$ of the line.

1. Problem Description

The problem requires us to convert the equation $3x - 2y = -6$ into slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Then, we need to identify the slope $m$ of the line.

2. Solution Steps

First, we rearrange the equation $3x - 2y = -6$ to solve for $y$.

$3x - 2y = -6$

Subtract $3x$ from both sides:

$-2y = -3x - 6$

Divide both sides by $-2$:

$y = \frac{-3x - 6}{-2}$

$y = \frac{-3x}{-2} + \frac{-6}{-2}$

$y = \frac{3}{2}x + 3$

The equation is now in slope-intercept form, $y = \frac{3}{2}x + 3$.

The slope $m$ is the coefficient of $x$, which is $\frac{3}{2}$.

3. Final Answer

$\frac{3}{2}$