For each pair of linear equations given below, drawn graphs and then state, whether the lines drawn are parallel or perpendicular to each other.
`2x-3y=6`
`3x+4y=24`
`x/4+y/3=1`

Answer

To solve the problem, we need to analyze the given linear equations, convert them into a suitable form, plot their graphs, and then determine the relationship between the lines (whether they are parallel or perpendicular).

### Step-by-Step Solution:

**Step 1: Convert the equations into intercept form.**

The intercept form of a linear equation is given by:
\[ \frac{x}{a} + \frac{y}{b} = 1 \]

**For the first equation:**
\[ 2x - 3y = 6 \]
We can rearrange it:
\[ 2x = 3y + 6 \implies y = \frac{2}{3}x - 2 \]
To convert it to intercept form, we can express it as:
\[ \frac{x}{3} + \frac{y}{-2} = 1 \]
So, \( a = 3 \) and \( b = -2 \).

**For the second equation:**
\[ 3x + 4y = 24 \]
Rearranging gives:
\[ 4y = -3x + 24 \implies y = -\frac{3}{4}x + 6 \]
To convert it to intercept form, we divide by 24:
\[ \frac{x}{8} + \frac{y}{6} = 1 \]
So, \( a = 8 \) and \( b = 6 \).

**For the third equation:**
\[ \frac{x}{4} + \frac{y}{3} = 1 \]
This is already in intercept form with \( a = 4 \) and \( b = 3 \).

**Step 2: Plot the graphs of the equations.**

1. **Graph of Line 1 (L1):**
- Intercepts: \( (3, 0) \) and \( (0, -2) \)
- Plot the points and draw the line.

2. **Graph of Line 2 (L2):**
- Intercepts: \( (8, 0) \) and \( (0, 6) \)
- Plot the points and draw the line.

3. **Graph of Line 3 (L3):**
- Intercepts: \( (4, 0) \) and \( (0, 3) \)
- Plot the points and draw the line.

**Step 3: Analyze the graphs.**

- **L1:** Slope = \( \frac{2}{3} \)
- **L2:** Slope = \( -\frac{3}{4} \)
- **L3:** Slope = \( -\frac{3}{4} \)

**Step 4: Determine the relationship between the lines.**

- **L1 and L2:** The slopes are different, so they are neither parallel nor perpendicular.
- **L2 and L3:** The slopes are the same (\(-\frac{3}{4}\)), so they are parallel.

### Conclusion:
- Lines L2 and L3 are parallel.
- Line L1 is neither parallel nor perpendicular to L2 or L3.