Find the slope of the line which is parallel to :
`x + 2y + 3 = 0 `

Answer

To find the slope of the line which is parallel to the given line represented by the equation \(x + 2y + 3 = 0\), we will follow these steps:

### Step 1: Write the equation in slope-intercept form
We start with the equation:
\[ x + 2y + 3 = 0 \]
To express this in the slope-intercept form \(y = mx + c\), we need to isolate \(y\).

### Step 2: Rearrange the equation
Subtract \(x\) and \(3\) from both sides:
\[ 2y = -x - 3 \]

### Step 3: Divide by the coefficient of \(y\)
Now, divide every term by \(2\) to solve for \(y\):
\[ y = -\frac{1}{2}x - \frac{3}{2} \]

### Step 4: Identify the slope
In the slope-intercept form \(y = mx + c\), the coefficient \(m\) represents the slope of the line. From our equation:
\[ y = -\frac{1}{2}x - \frac{3}{2} \]
we can see that the slope \(m\) is:
\[ m = -\frac{1}{2} \]

### Step 5: Conclusion about parallel lines
Since parallel lines have the same slope, the slope of the line that is parallel to the given line is also:
\[ -\frac{1}{2} \]

### Final Answer
The slope of the line which is parallel to the line \(x + 2y + 3 = 0\) is \(-\frac{1}{2}\).

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