The problem asks us to convert the linear equation $3x - 2y = -6$ into slope-intercept form, and then identify the slope and y-intercept of the line.

1. Problem Description

The problem asks us to convert the linear equation $3x - 2y = -6$ into slope-intercept form, and then identify the slope and y-intercept of the line.

2. Solution Steps

First, we need to rewrite the equation $3x - 2y = -6$ in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Subtract $3x$ from both sides of the equation:

$-2y = -3x - 6$

Divide both sides by $-2$:

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

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

So the slope-intercept form of the equation is $y = \frac{3}{2}x + 3$.

Now, we can identify the slope and the y-intercept.

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

The y-intercept $b$ is the constant term, so $b = 3$.

The y-intercept as a coordinate point is $(0, 3)$.

3. Final Answer

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

$m = \frac{3}{2}$

$(0, 3)$