Write down the slopes of the lines parallel to the line joining A(-1, 5) and B(-6, -7)

Answer

To find the slopes of the lines parallel to the line joining the points A(-1, 5) and B(-6, -7), we will follow these steps:

### Step 1: Identify the coordinates of points A and B
We have the coordinates of point A as (-1, 5) and point B as (-6, -7).

### Step 2: Use the slope formula
The formula for the slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

### Step 3: Assign the coordinates
Let:
- \( A(x_1, y_1) = (-1, 5) \)
- \( B(x_2, y_2) = (-6, -7) \)

### Step 4: Substitute the coordinates into the slope formula
Substituting the coordinates into the slope formula:
\[ m = \frac{-7 - 5}{-6 - (-1)} \]

### Step 5: Simplify the expression
Calculating the numerator and denominator:
- Numerator: \( -7 - 5 = -12 \)
- Denominator: \( -6 + 1 = -5 \)

So, the slope becomes:
\[ m = \frac{-12}{-5} = \frac{12}{5} \]

### Step 6: State the slope of the line AB
The slope of the line joining points A and B is \( \frac{12}{5} \).

### Step 7: Find the slope of the lines parallel to line AB
Since parallel lines have the same slope, the slope of any line parallel to line AB will also be \( \frac{12}{5} \).

### Final Answer
The slope of the lines parallel to the line joining A(-1, 5) and B(-6, -7) is \( \frac{12}{5} \).

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