Question

from the given slopes of the lines, identify whether the two lines are parallel, perpendicular, or neither.

1. slope of line 1: 11, slope of line 2: -11
2. slope of line 1: $\frac{3}{5}$, slope of line 2: $-\frac{3}{5}$
3. slope of line 1: 7, slope of line 2: $-\frac{1}{7}$
4. slope of line 1: $\frac{3}{5}$, slope of line 2: $-\frac{3}{5}$
5. slope of line 1: 7, slope of line 2: $-\frac{1}{7}$

Explanation:

Step1: Recall parallel/perpendicular rules

Parallel: $m_1 = m_2$; Perpendicular: $m_1 \times m_2 = -1$

Step2: Analyze pair 1

Slopes: $11$ and $-11$. $11
eq -11$, $11 \times (-11) = -121
eq -1$

Step3: Analyze pair 2

Slopes: $\frac{3}{5}$ and $-\frac{3}{5}$. $\frac{3}{5}
eq -\frac{3}{5}$, $\frac{3}{5} \times (-\frac{3}{5}) = -\frac{9}{25}
eq -1$

Step4: Analyze pair 3

Slopes: $7$ and $-\frac{1}{7}$. $7 \times (-\frac{1}{7}) = -1$

Step5: Analyze pair 4

Slopes: $\frac{3}{5}$ and $-\frac{3}{5}$. $\frac{3}{5}
eq -\frac{3}{5}$, $\frac{3}{5} \times (-\frac{3}{5}) = -\frac{9}{25}
eq -1$

Step6: Analyze pair 5

Slopes: $7$ and $-\frac{1}{7}$. $7 \times (-\frac{1}{7}) = -1$

Answer:

1. Neither
2. Neither
3. Perpendicular
4. Neither
5. Perpendicular