If the line y+2x+3=0 is parallel to the line 2y-px-4=0 , what is the value of p ?

Options

A. `-4`
B. `-2`
C. 2
D. 4

Answer

To solve the problem, we need to find the value of \( p \) such that the two lines are parallel. For two lines to be parallel, their slopes must be equal.

### Step-by-Step Solution:

1. **Identify the first line**: The first line is given by the equation:
\[ y + 2x + 3 = 0 \]
We can rearrange this into the slope-intercept form \( y = mx + c \).

2. **Rearranging the first line**:
\[ y = -2x - 3 \]
From this equation, we can see that the slope \( m_1 \) of the first line is:
\[ m_1 = -2 \]

3. **Identify the second line**: The second line is given by the equation:
\[ 2y - px - 4 = 0 \]
We will also rearrange this into the slope-intercept form.

4. **Rearranging the second line**:
\[ 2y = px + 4 \]
Dividing everything by 2:
\[ y = \frac{p}{2}x + 2 \]
From this equation, we can see that the slope \( m_2 \) of the second line is:
\[ m_2 = \frac{p}{2} \]

5. **Setting the slopes equal**: Since the lines are parallel, we set their slopes equal to each other:
\[ m_1 = m_2 \]
Therefore:
\[ -2 = \frac{p}{2} \]

6. **Solving for \( p \)**: To find \( p \), we multiply both sides of the equation by 2:
\[ -4 = p \]

Thus, the value of \( p \) is:
\[ \boxed{-4} \]