If 7x + 3y + 9 = 0 and y = kx + 7 are two parallel lines then find the value of k.
(a)9/7
(b)-7/3
(c)5/8
(d)6/5

Answer

To solve the problem, we need to find the value of \( k \) such that the lines represented by the equations \( 7x + 3y + 9 = 0 \) and \( y = kx + 7 \) are parallel.

### Step-by-Step Solution:

1. **Identify the slope of the second line**:
The second line is given in the slope-intercept form \( y = kx + 7 \). Here, the slope \( m_2 \) is simply \( k \).

**Hint**: Remember that in the equation \( y = mx + c \), \( m \) represents the slope.

2. **Rearrange the first line to slope-intercept form**:
We start with the equation \( 7x + 3y + 9 = 0 \). To convert this into the slope-intercept form \( y = mx + c \), we need to isolate \( y \):
\[ 3y = -7x - 9 \]
Now, divide everything by 3:
\[ y = -\frac{7}{3}x - 3 \]
Here, the slope \( m_1 \) of the first line is \( -\frac{7}{3} \).

**Hint**: To find the slope, isolate \( y \) on one side of the equation.

3. **Set the slopes equal to each other**:
Since the two lines are parallel, their slopes must be equal:
\[ m_1 = m_2 \]
Substituting the values we found:
\[ -\frac{7}{3} = k \]

**Hint**: For parallel lines, the slopes must be equal.

4. **Conclusion**:
Therefore, the value of \( k \) is:
\[ k = -\frac{7}{3} \]

Thus, the correct answer is option (b) \( -\frac{7}{3} \).