Find the slope of the line which is perpendicular to :
`x/3 -  2y = 4 `

Answer

To find the slope of the line that is perpendicular to the given line represented by the equation \( \frac{x}{3} - 2y = 4 \), we will follow these steps:

### Step 1: Rearrange the equation into slope-intercept form
The first step is to rearrange the given equation into the slope-intercept form, which is \( y = mx + c \), where \( m \) is the slope.

Starting with the equation:
\[ \frac{x}{3} - 2y = 4 \]

Multiply through by 3 to eliminate the fraction:
\[ x - 6y = 12 \]

Now, isolate \( y \):
\[ -6y = -x + 12 \]

Dividing everything by -6 gives:
\[ y = \frac{1}{6}x - 2 \]

### Step 2: Identify the slope of the given line
From the equation \( y = \frac{1}{6}x - 2 \), we can see that the slope \( m_1 \) of the given line is:
\[ m_1 = \frac{1}{6} \]

### Step 3: Use the relationship between slopes of perpendicular lines
The slopes of two perpendicular lines are related by the equation:
\[ m_1 \cdot m_2 = -1 \]

Where \( m_1 \) is the slope of the first line and \( m_2 \) is the slope of the perpendicular line. We can rearrange this to find \( m_2 \):
\[ m_2 = -\frac{1}{m_1} \]

### Step 4: Calculate the slope of the perpendicular line
Substituting \( m_1 = \frac{1}{6} \) into the equation gives:
\[ m_2 = -\frac{1}{\frac{1}{6}} = -6 \]

### Final Answer
Thus, the slope of the line that is perpendicular to the given line is:
\[ \boxed{-6} \]