Question

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

	slope of line 1	slope of line 2	answer
1)	10	\\(\frac{1}{10}\\)	neither
2)	8	8
3)	3	\\(-\frac{1}{3}\\)	perpendicular
4)	10	\\(\frac{1}{10}\\)
5)	\\(\frac{2}{5}\\)	\\(-\frac{2}{5}\\)	neither
6)	8	8
7)	3	\\(-\frac{1}{3}\\)	perpendicular
8)	\\(\frac{3}{5}\\)	\\(-\frac{5}{3}\\)	perpendicular
9)	5	-5
10)	\\(\frac{4}{5}\\)	\\(\frac{4}{5}\\)

Explanation:

Step1: Recall parallel/perpendicular rules

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

Step2: Solve row 2

Check if slopes are equal: $8=8$

Step3: Solve row 4

Multiply slopes: $10 \times \frac{1}{10}=1
eq -1$, slopes not equal

Step4: Solve row 6

Check if slopes are equal: $8=8$

Step5: Solve row 9

Multiply slopes: $5 \times (-5)=-25
eq -1$, slopes not equal

Step6: Solve row 10

Check if slopes are equal: $\frac{4}{5}=\frac{4}{5}$

Answer:

1. neither
2. parallel
3. perpendicular
4. neither
5. neither
6. parallel
7. perpendicular
8. perpendicular
9. neither
10. parallel