Write down the slope of the line
perpendicular to the line joining B(2, -3) and S(-4, 1).

Answer

To find the slope of the line perpendicular to the line joining points B(2, -3) and S(-4, 1), we will follow these steps:

### Step 1: Identify the coordinates of points B and S
- Point B has coordinates (2, -3)
- Point S has coordinates (-4, 1)

### Step 2: Calculate the slope of the line joining points B and S
The formula for the slope (m) between two points (x1, y1) and (x2, y2) is given by:
\[ m = \frac{y2 - y1}{x2 - x1} \]
Here, we can assign:
- \(x1 = 2\), \(y1 = -3\)
- \(x2 = -4\), \(y2 = 1\)

Substituting these values into the formula:
\[ m_{BS} = \frac{1 - (-3)}{-4 - 2} = \frac{1 + 3}{-4 - 2} = \frac{4}{-6} = -\frac{2}{3} \]

### Step 3: Determine the slope of the line perpendicular to BS
The slope of a line that is perpendicular to another line is the negative reciprocal of the slope of the original line. If the slope of line BS is \(m_{BS}\), then the slope \(m\) of the perpendicular line is given by:
\[ m \cdot m_{BS} = -1 \]
Substituting \(m_{BS} = -\frac{2}{3}\):
\[ m \cdot \left(-\frac{2}{3}\right) = -1 \]

### Step 4: Solve for the slope of the perpendicular line
To find \(m\), we can rearrange the equation:
\[ m = \frac{-1}{-\frac{2}{3}} = \frac{3}{2} \]

### Conclusion
The slope of the line perpendicular to the line joining points B and S is:
\[ \boxed{\frac{3}{2}} \]