Find the slope of the line through the points `(4,-6)(-2,-5)`

Answer

To find the slope of the line through the points (4, -6) and (-2, -5), we can use the formula for the slope (m) of a line that passes through two points (x1, y1) and (x2, y2):

\[ m = \frac{y2 - y1}{x2 - x1} \]

### Step-by-Step Solution:

1. **Identify the coordinates of the points:**
- Let point A = (4, -6) → here, \( x_1 = 4 \) and \( y_1 = -6 \)
- Let point B = (-2, -5) → here, \( x_2 = -2 \) and \( y_2 = -5 \)

2. **Substitute the values into the slope formula:**
\[ m = \frac{y2 - y1}{x2 - x1} = \frac{-5 - (-6)}{-2 - 4} \]

3. **Simplify the numerator:**
- Calculate \( -5 - (-6) \):
\[ -5 + 6 = 1 \]

4. **Simplify the denominator:**
- Calculate \( -2 - 4 \):
\[ -2 - 4 = -6 \]

5. **Combine the results:**
\[ m = \frac{1}{-6} = -\frac{1}{6} \]

### Final Answer:
The slope of the line through the points (4, -6) and (-2, -5) is \( -\frac{1}{6} \).