- Parallel: y = 3x - 7 and y = 3x + 1
- Perpendicular: y = -2/5x + 3 and y = 5/2x + 8
- Neither: y = -1/4x and y = 4x - 5
- Parallel: 2x + 7y = 28 and 7x - 2y = 4 (slopes are -2/7 and 7/2, so perpendicular)
- Perpendicular: y = -5x + 1 and x - 5y = 30 (slope of second is 1/5, so perpendicular to first)
- Neither: 3x + 2y = 8 and 2x + 3y = -12 (slopes -3/2 and -2/3, not equal or negative reciprocals)
- Parallel: y = -4x - 1 and 8x + 2y = 14 (second equation simplifies to y = -4x + 7, same slope)
- Perpendicular: x + y = 7 and x - y = 9 (slopes -1 and 1, negative reciprocals)
- Neither: y = 1/3x + 9 and x - 3y = 3 (second equation simplifies to y = 1/3x - 1, same slope — should be parallel)
- Parallel: 4x + 9y = 18 and y = 4x + 9 (first has slope -4/9, second has slope 4 — neither)
- Perpendicular: 5x - 10y = 20 and y = -2x + 6 (first simplifies to y = 0.5x - 2, slope 0.5; second slope -2 — negative reciprocals)
- Neither: -9x + 12y = 24 and y = 3/4x - 5 (first simplifies to y = 3/4x + 2, same slope as second — should be parallel)
- Parallel: y = x - 3 and x - y = 8 (second simplifies to y = x - 8, same slope)
- Perpendicular: 10x + 8y = 16 and 5y = 4x - 15 (first simplifies to y = -5/4x + 2, second to y = 4/5x - 3 — slopes are negative reciprocals)
- Neither: y = 5/3x + 7 and 6x - 10y = 10 (second simplifies to y = 3/5x - 1, slopes 5/3 and 3/5 — neither)
- Parallel: x - 2y = 18 and 2x + y = 6 (first has slope 1/2, second has slope -2 — perpendicular)
- Parallel: x = 4 and x = -6 (both vertical — parallel)
- Neither: x = 1 and y = -8 (one vertical, one horizontal — perpendicular)
Parent Tip: Review the logic above to help your child master the concept of parallel perpendicular or neither worksheet answers.