Find the slope of the line which is parallel to :
`x/2 - y/3 - 1 = 0`

Answer

To find the slope of the line that is parallel to the given line \( \frac{x}{2} - \frac{y}{3} - 1 = 0 \), we will follow these steps:

### Step 1: Rewrite the equation in standard form
Start with the given equation:
\[ \frac{x}{2} - \frac{y}{3} - 1 = 0 \]
To eliminate the fractions, we can multiply the entire equation by 6 (the least common multiple of 2 and 3):
\[ 6 \left( \frac{x}{2} \right) - 6 \left( \frac{y}{3} \right) - 6(1) = 0 \]
This simplifies to:
\[ 3x - 2y - 6 = 0 \]

### Step 2: Rearrange the equation to find the slope
Next, we rearrange the equation into the slope-intercept form \( y = mx + c \):
\[ 3x - 2y = 6 \]
Now, isolate \( y \):
\[ -2y = -3x + 6 \]
Dividing by -2 gives:
\[ y = \frac{3}{2}x - 3 \]

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

### Step 4: Conclusion
Since parallel lines have the same slope, the slope of the line that is parallel to the given line is:
\[ \text{slope} = \frac{3}{2} \]