- Parallel lines have the same slope.
- Perpendicular lines have slopes that are negative reciprocals (their product is -1).
- If slopes are different and not negative reciprocals, the lines are neither parallel nor perpendicular.
1. y = 1/2x → slope = 1/2
2. y = -1/3x - 1 → slope = -1/3
3. y = x → slope = 1
4. y = 5x - 13 → slope = 5
5. y = 1/4x → slope = 1/4
6. y = -1/7x - 5 → slope = -1/7
7. y = 3x - 4 → slope = 3
8. y = -4x - 5 → slope = -4
9. y = -1/2x - 1 → slope = -1/2
10. y = -1/3x + 5 → slope = -1/3
11. y = 1/5x + 8 → slope = 1/5
12. y = 2x + 5 → slope = 2
13. y = -1/6x → slope = -1/6
14. y = x - 11 → slope = 1
15. neither → no match for slope or negative reciprocal
16. Perpendicular → slopes multiply to -1 (e.g., 1/2 and -2, but here: 2 and -1/2? Check pairs)
17. parallel → same slope (e.g., 2 and 2? Or -1/3 and -1/3)
18. neither → no match
19. neither → no match
20. Parallel → same slope
Matching:
- Lines 2 and 10 both have slope -1/3 → parallel → #17
- Lines 3 and 14 both have slope 1 → parallel → #20
- Line 1 (slope 1/2) and Line 9 (slope -1/2): (1/2)*(-1/2) = -1/4 ≠ -1 → not perpendicular
Wait — check Line 12 (slope 2) and Line 9 (slope -1/2): 2 * (-1/2) = -1 → perpendicular → #16
- Line 1 (1/2) and Line 12 (2): (1/2)*2 = 1 ≠ -1 → not perpendicular
- Line 8 (slope -4) and Line 11 (slope 1/5): (-4)*(1/5) = -4/5 ≠ -1 → neither → #18
- Line 7 (slope 3) and Line 13 (slope -1/6): 3*(-1/6) = -1/2 ≠ -1 → neither → #19
- Line 4 (slope 5) and Line 11 (slope 1/5): 5*(1/5)=1 ≠ -1 → not perpendicular
But 5 and -1/5 would be perpendicular — no line has slope -1/5.
Line 11 slope 1/5, is there a line with slope -5? No.
So #15 must be for a pair like Line 5 (1/4) and Line 6 (-1/7): different, not negative reciprocals → neither.
Final matching based on key positions:
#15: neither → e.g., Line 5 and Line 6
#16: Perpendicular → Line 9 and Line 12 (slopes -1/2 and 2)
#17: parallel → Line 2 and Line 10 (both -1/3)
#18: neither → e.g., Line 8 and Line 11
#19: neither → e.g., Line 7 and Line 13
#20: Parallel → Line 3 and Line 14 (both slope 1)
The key labels correspond to the relationships between specific pairs. The solution matches the given key by identifying which line pairs are parallel, perpendicular, or neither based on their slopes.
Parent Tip: Review the logic above to help your child master the concept of writing equations of parallel and perpendicular lines worksheet answer key.
