Write down the slopes of the following lines:
`3x+4y-2(x+x_(1))-5(y+y_(1))+2=0`

Answer

To find the slope of the line given by the equation \(3x + 4y - 2(x + x_1) - 5(y + y_1) + 2 = 0\), we will convert it into the slope-intercept form, which is \(y = mx + c\), where \(m\) is the slope.

### Step-by-step Solution:

1. **Start with the given equation:**
\[ 3x + 4y - 2(x + x_1) - 5(y + y_1) + 2 = 0 \]

2. **Distribute the terms inside the parentheses:**
\[ 3x + 4y - 2x - 2x_1 - 5y - 5y_1 + 2 = 0 \]

3. **Combine like terms:**
- Combine the \(x\) terms: \(3x - 2x = x\)
- Combine the \(y\) terms: \(4y - 5y = -y\)
\[ x - y - 2x_1 - 5y_1 + 2 = 0 \]

4. **Rearrange the equation to isolate \(y\):**
\[ -y = -x + 2x_1 + 5y_1 - 2 \]
Now, multiply the entire equation by \(-1\):
\[ y = x - 2x_1 - 5y_1 + 2 \]

5. **Identify the slope \(m\):**
In the equation \(y = mx + c\), the coefficient of \(x\) is the slope \(m\). Here, the coefficient of \(x\) is \(1\).
\[ m = 1 \]

6. **Conclusion:**
The slope of the line is:
\[ \text{slope} = 1 \]