Find the slope and the y-intercept of the lines.
` 3x+2y =6`.

Answer

To find the slope and the y-intercept of the line given by the equation \(3x + 2y = 6\), we will rearrange the equation into the slope-intercept form, which is \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept.

### Step-by-step Solution:

1. **Start with the original equation:**
\[ 3x + 2y = 6 \]

**Hint:** Identify the equation you need to manipulate.

2. **Isolate the term with \(y\):**
Subtract \(3x\) from both sides:
\[ 2y = 6 - 3x \]

**Hint:** You want to get \(y\) by itself on one side of the equation.

3. **Divide all terms by 2 to solve for \(y\):**
\[ y = \frac{6 - 3x}{2} \]
This can be simplified to:
\[ y = -\frac{3}{2}x + \frac{6}{2} \]

**Hint:** Remember to distribute the division across both terms in the numerator.

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

**Hint:** Combine like terms to simplify your expression.

5. **Identify the slope and y-intercept:**
From the equation \(y = -\frac{3}{2}x + 3\):
- The slope \(m\) is \(-\frac{3}{2}\)
- The y-intercept \(c\) is \(3\)

**Hint:** Compare your equation to the standard slope-intercept form to find \(m\) and \(c\).

### Final Answer:
- Slope \(m = -\frac{3}{2}\)
- Y-intercept \(c = 3\)