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

Answer

To find the slope of the line that passes through the points \( (4, -6) \) and \( (-2, -5) \), we can use the formula for the slope \( m \) of a line given two points \( (x_1, y_1) \) and \( (x_2, y_2) \):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

### Step 1: Identify the coordinates
Let:
- \( (x_1, y_1) = (4, -6) \)
- \( (x_2, y_2) = (-2, -5) \)

### Step 2: Substitute the coordinates into the slope formula
Substituting the values into the slope formula:

\[ m = \frac{-5 - (-6)}{-2 - 4} \]

### Step 3: Simplify the expression
Now simplify the numerator and the denominator:

- The numerator:
\[ -5 - (-6) = -5 + 6 = 1 \]

- The denominator:
\[ -2 - 4 = -6 \]

So, we have:

\[ m = \frac{1}{-6} \]

### Step 4: Finalize the slope
Thus, the slope \( m \) is:

\[ m = -\frac{1}{6} \]

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

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