Let's analyze and solve the problem step by step:

Line A:

The equation for Line A is given as: $-6x - 2y = 9$ We need to convert this to slope-intercept form ($y = mx + b$), where $m$ is the slope.

1. Isolate the term involving $y$: $-2y = 6x + 9$
2. Divide through by $-2$ to solve for $y$: $y = -3x - \frac{9}{2}$ Now we can see the slope of Line A is $m_A = -3$.

Line B:

The equation for Line B is given as: $y + 1 = -3(x - 9)$ We can simplify this by distributing the $-3$ on the right-hand side.

1. Distribute the $-3$: $y + 1 = -3x + 27$
2. Subtract 1 from both sides: $y = -3x + 26$ Now we can see that the slope of Line B is $m_B = -3$.

Conclusion:

Since both lines have the same slope ($m_A = m_B = -3$), they are parallel.

Final Answer:

• Slope of Line A: $-3$
• Slope of Line B: $-3$
• Line A and Line B are parallel.

Would you like any further details or clarifications?

Related Questions:

1. How do you determine if two lines are perpendicular based on their slopes?
2. What happens when two lines have slopes that are negative reciprocals?
3. How do you find the slope of a line given two points?
4. How does changing the slope of a line affect its steepness?
5. What is the significance of the y-intercept in the slope-intercept form of a line?

Tip:

For two lines to be perpendicular, their slopes must be negative reciprocals of each other, meaning $m_1 \times m_2 = -1$.