The problem asks us to find the slope $m$ and y-intercept $b$ of the line given by the equation $3x + 2y = 6$.

1. Problem Description

The problem asks us to find the slope $m$ and y-intercept $b$ of the line given by the equation $3x + 2y = 6$.

2. Solution Steps

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

The given equation is $3x + 2y = 6$.

Subtract $3x$ from both sides:

$2y = -3x + 6$

Divide both sides by $2$:

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

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

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

Comparing this equation with the slope-intercept form $y = mx + b$, we can identify the slope $m$ and the y-intercept $b$.

$m = -\frac{3}{2}$ and $b = 3$

3. Final Answer

The slope $m = -\frac{3}{2}$ and the y-intercept $b = 3$.

Therefore, the answer is (b).