A (5, 4), B (-3, -2) and C (1, -8) are the vertices of a triangle ABC. Find :
the slope of the line parallel to AC.

Answer

To find the slope of the line parallel to AC, we first need to calculate the slope of line AC using the coordinates of points A and C.

### Step-by-Step Solution:

1. **Identify the coordinates of points A and C:**
- A(5, 4)
- C(1, -8)

2. **Use the slope formula:**
The slope (m) of a line through two points (x1, y1) and (x2, y2) is given by:
\[ m = \frac{y2 - y1}{x2 - x1} \]

3. **Assign the coordinates:**
- Let A be (x1, y1) = (5, 4)
- Let C be (x2, y2) = (1, -8)

4. **Substitute the coordinates into the slope formula:**
\[ m_{AC} = \frac{-8 - 4}{1 - 5} \]

5. **Calculate the difference in y-coordinates:**
\[ -8 - 4 = -12 \]

6. **Calculate the difference in x-coordinates:**
\[ 1 - 5 = -4 \]

7. **Substitute these values back into the slope formula:**
\[ m_{AC} = \frac{-12}{-4} \]

8. **Simplify the slope:**
\[ m_{AC} = 3 \]

9. **Determine the slope of the line parallel to AC:**
Since parallel lines have the same slope, the slope of any line parallel to AC is also:
\[ m = 3 \]

### Final Answer:
The slope of the line parallel to AC is **3**.