- Parallel Lines have
equal slopes
- Perpendicular lines have
negative reciprocal slopes
1. The given line is `y = 10x - 3`. Its slope is 10.
A parallel line has the same slope, so its slope is also 10.
Using point-slope form with point (1, 5): `y - 5 = 10(x - 1)`
Simplify to slope-intercept form: `y = 10x - 10 + 5` → `y = 10x - 5`
2. The given line is `y = -4x - 5`. Its slope is -4.
A parallel line has the same slope, so its slope is also -4.
Using point-slope form with point (0, -1): `y - (-1) = -4(x - 0)`
Simplify to slope-intercept form: `y + 1 = -4x` → `y = -4x - 1`
3. The given line is `y = -5/8x`. Its slope is -5/8.
A perpendicular line has a slope that is the negative reciprocal: `-1 / (-5/8) = 8/5`.
Using point-slope form with point (-5, -3): `y - (-3) = (8/5)(x - (-5))`
Simplify: `y + 3 = (8/5)(x + 5)`
Distribute: `y + 3 = (8/5)x + 8`
Solve for y: `y = (8/5)x + 8 - 3` → `y = (8/5)x + 5`
4. The given line is `y = -x - 5`. Its slope is -1.
A perpendicular line has a slope that is the negative reciprocal: `-1 / (-1) = 1`.
Using point-slope form with point (-5, -1): `y - (-1) = 1(x - (-5))`
Simplify: `y + 1 = x + 5`
Solve for y: `y = x + 5 - 1` → `y = x + 4`
Parent Tip: Review the logic above to help your child master the concept of slope of parallel and perpendicular lines worksheet.
