The problem asks us to determine whether pairs of slopes are parallel, perpendicular, or neither. We are given 6 pairs of slopes, and we need to classify their relationship.

1. Problem Description

The problem asks us to determine whether pairs of slopes are parallel, perpendicular, or neither. We are given 6 pairs of slopes, and we need to classify their relationship.

2. Solution Steps

Two lines are parallel if and only if they have the same slope.

Two lines are perpendicular if and only if the product of their slopes is $-1$.

1. $m_1 = 2$ and $m_2 = -\frac{1}{2}$. The product of the slopes is $2 \cdot (-\frac{1}{2}) = -1$. Therefore, the lines are perpendicular.

2. $m_1 = 3$ and $m_2 = -3$. The slopes are not equal, so they are not parallel. The product of the slopes is $3 \cdot (-3) = -9$, which is not $-1$, so they are not perpendicular. Therefore, the lines are neither parallel nor perpendicular.

3. $m_1 = -4$ and $m_2 = -\frac{1}{4}$. The slopes are not equal, so they are not parallel. The product of the slopes is $-4 \cdot (-\frac{1}{4}) = 1$, which is not $-1$, so they are not perpendicular. Therefore, the lines are neither parallel nor perpendicular.

4. $m_1 = 10$ and $m_2 = -0.1 = -\frac{1}{10}$. The slopes are not equal, so they are not parallel. The product of the slopes is $10 \cdot (-\frac{1}{10}) = -1$. Therefore, the lines are perpendicular.

5. $m_1 = 2$ and $m_2 = 3$. The slopes are not equal, so they are not parallel. The product of the slopes is $2 \cdot 3 = 6$, which is not $-1$, so they are not perpendicular. Therefore, the lines are neither parallel nor perpendicular.

6. $m_1 = \frac{4}{5}$ and $m_2 = \frac{8}{10}$. Since $\frac{8}{10} = \frac{4}{5}$, the slopes are equal. Therefore, the lines are parallel.

3. Final Answer

1. Perpendicular

2. Neither

3. Neither

4. Perpendicular

5. Neither

6. Parallel